Hvac system design and operational tool for building infection control

ABSTRACT

A heating, ventilation, or air conditioning system (HVAC) design and operational tool includes one or more processors and memory storing instructions that, when executed by the one or more processors, cause the one or more processors to perform operations including obtaining a dynamic temperature model and a dynamic infectious quanta model for one or more building zones, determining an infection probability, and performing a plurality of simulations for a plurality of different equipment configurations using the dynamic temperature model, the dynamic infectious quanta model, and the infection probability to generate results. The operations include generating, using the results of the plurality of simulations, at least one of design including one or more recommended design parameters data or operational data including one or more recommended operational parameters for the HVAC system and initiating an automated action using at least one of the design data or the operational data.

CROSS-REFERENCE TO RELATED PATENT APPLICATIONS

This application is a Continuation of U.S. application Ser. No.16/927,766, filed Jul. 13, 2020, which claims the benefit of andpriority to U.S. Provisional Patent Application No. 62/873,631, filedJul. 12, 2019, and U.S. Provisional Patent Application No. 63/044,906,filed Jun. 26, 2020, all of which are incorporated herein by referencein their entireties.

BACKGROUND

The present disclosure relates generally to a building system in abuilding. The present disclosure relates more particularly tomaintaining occupant comfort in a building through environmentalcontrol.

Maintaining occupant comfort and disinfection in a building requiresbuilding equipment (e.g., HVAC equipment) to be operated to changeenvironmental conditions in the building. In some systems, occupants arerequired to make any desired changes to the environmental conditionsthemselves if they are not comfortable. When operating buildingequipment to change specific environmental conditions, otherenvironmental conditions may be affected as a result. Maintainingoccupant comfort and disinfection can be expensive if not performedcorrectly. Thus, systems and methods are needed to maintain occupantcomfort and provide sufficient disinfection for multiple environmentalconditions while reducing expenses related to maintaining occupantcomfort and disinfection.

SUMMARY

One implementation of the present disclosure is a heating, ventilation,or air conditioning (HVAC) system for one or more building zones. TheHVAC system includes airside HVAC equipment operable to provide cleanair to the one or more building zones and a controller. The controlleris configured to obtain a dynamic temperature model and a dynamicinfectious quanta model for the one or more building zones, determine aninfection probability, and generate control decisions for the airsideHVAC equipment using the dynamic temperature model, the dynamicinfectious quanta model, and the infection probability. In someembodiments, the control decisions provide a desired level ofdisinfection. In some embodiments, the control decisions indicate anamount of the clean air to be provided to the one or more building zonesby the airside HVAC equipment. Obtaining the dynamic temperature modeland the dynamic infectious quanta model can include receiving one orboth of the models as inputs, generating one or both of the models,retrieving one or both of the models from a database or from a userdevice, or otherwise obtaining one or both of the models in any othermanner.

In some embodiments, the airside HVAC equipment includes disinfectionlighting operable to disinfect the clean air before it is provided tothe one or more building zones and one or more filters configured tofilter the clean air before it is provided to the one or more buildingzones.

In some embodiments, the controller is configured to receive a desiredlevel of disinfection via a user interface and generate a thresholdvalue for the infection probability using the desired level ofdisinfection.

In some embodiments, the controller is configured to obtain a dynamichumidity model for the one or more building zones and use the dynamichumidity model, in addition to the dynamic temperature model and thedynamic infectious quanta model, to generate the control decisions.

In some embodiments, the one or more building zones include a pluralityof building zones and the dynamic temperature model and the dynamicinfectious quanta model are either individual dynamic models for each ofthe plurality of building zones or aggregate dynamic models for theplurality of building zones based on a weighted volume average of theplurality of zones.

In some embodiments, using the dynamic temperature model, the dynamicinfectious quanta model, and the infection probability to generate thecontrol decisions includes generating optimization constraints based onthe dynamic temperature model, the dynamic infectious quanta model, andthe infection probability and performing an optimization of an objectivefunction subject to the optimization constraints to generate the controldecisions as results of the optimization.

Another implementation of the present disclosure is a controller for aheating, ventilation, or air conditioning (HVAC) system of a building.The controller includes one or more processors and memory storinginstructions that, when executed by the one or more processors, causethe one or more processors to perform operations including obtaining adynamic temperature model and a dynamic infectious quanta model for oneor more building zones of the building, determining an infectionprobability, and generating control decisions using the dynamictemperature model, the dynamic infectious quanta model, and theinfection probability. The operations further include using the controldecisions to operate at least one of disinfection lighting, a variableair volume (VAV) unit, or an air handling unit (AHU) of the HVAC system.In some embodiments, the control decisions provide a desired level ofdisinfection. In some embodiments, the control decisions indicate anamount of the clean air to be provided to the one or more buildingzones. Obtaining the dynamic temperature model and the dynamicinfectious quanta model can include receiving one or both of the modelsas inputs, generating one or both of the models, retrieving one or bothof the models from a database or from a user device, or otherwiseobtaining one or both of the models in any other manner.

In some embodiments, the controller is configured to receive a desiredlevel of disinfection via a user interface and generate a thresholdvalue for the infection probability using the desired level ofdisinfection

In some embodiments, the control signals are generated using aconstraint on infectious quanta concentration based on a Wells-RileyEquation.

In some embodiments, the operations further include obtaining a dynamichumidity model for the one or more building zones and using the dynamichumidity model, in addition to the dynamic temperature model and thedynamic infectious quanta model, to generate the control decisions.

In some embodiments, the one or more building zones include a pluralityof building zones and the dynamic temperature model and the dynamicinfectious quanta model are either individual dynamic models for each ofthe plurality of building zones or aggregate dynamic models based on aweighted volume average of the plurality of building zones.

In some embodiments, using the dynamic temperature model, the dynamicinfectious quanta model, and the infection probability to generate thecontrol decisions includes generating optimization constraints based onthe dynamic temperature model, the dynamic infectious quanta model, andthe infection probability and performing an optimization of an objectivefunction subject to the optimization constraints to generate the controldecisions as results of the optimization.

In some embodiments, the control decisions indicate an amount of cleanair to be provided to the one or more building zones and using thecontrol decisions to operate the VAV unit includes generating both atemperature setpoint and a minimum airflow constraint for the VAV unit.The minimum airflow constraint may be the amount of clean air to beprovided to the one or more building zones. Using the control decisionsto operate the VAV unit may further include operating the VAV unit tocontrol a temperature of the one or more building zones based on thetemperature setpoint, subject to the minimum airflow constraint.

Another implementation of the present disclosure is a method forcontrolling building equipment to provide a desired level ofdisinfection. The method includes obtaining a dynamic temperature modeland dynamic infectious quanta model for one or more building zones,determining an infection probability, and generating control decisionsusing the dynamic temperature model, the dynamic infectious quantamodel, and the infection probability. The method includes using thecontrol decisions to operate the building equipment to provide theamount of clean air to the one or more building zones. In someembodiments, the control decisions provide the desired level ofdisinfection. In some embodiments, the control decisions indicate anamount of clean air to be provided to the one or more building zones bythe building equipment. Obtaining the dynamic temperature model and thedynamic infectious quanta model can include receiving one or both of themodels as inputs, generating one or both of the models, retrieving oneor both of the models from a database or from a user device, orotherwise obtaining one or both of the models in any other manner.

In some embodiments, using the dynamic temperature model, the dynamicinfectious quanta model, and the infection probability to generate thecontrol decisions includes generating optimization constraints based onthe dynamic temperature model, the dynamic infectious quanta model, andthe infection probability and performing an optimization of an objectivefunction subject to the optimization constraints to generate the controldecisions as results of the optimization.

In some embodiments, the controller is configured to receive the desiredlevel of disinfection via a user interface and generate a thresholdvalue for the infection probability using the desired level ofdisinfection.

In some embodiments, the method includes obtaining a dynamic humiditymodel for the one or more building zones and using the dynamic humiditymodel, in addition to the dynamic temperature model and the dynamicinfectious quanta model, to generate the control decisions.

In some embodiments, the one or more building zones include a pluralityof building zones and the dynamic temperature model and the dynamicinfectious quanta model are either individual dynamic models for each ofthe plurality of building zones or aggregate dynamic models based on aweighted volume average of the plurality of building zones.

In some embodiments, the building equipment include at least one ofdisinfection lighting, a filter, an air handling unit (AHU), or avariable air volume (VAV) unit.

In some embodiments, the control decisions include at least one ofcommands to actuate the disinfection lighting between an on state and anoff state, a fresh air intake fraction of the AHU, or an amount ofairflow for the VAV unit to provide to the one or more building zones.

Another implementation of the present disclosure is a heating,ventilation, or air conditioning (HVAC) system for one or more buildingzones. The HVAC system includes airside HVAC equipment operable toprovide clean air to the one or more building zones and a controller.The controller is configured to obtain a dynamic infectious quanta modelfor the one or more building zones, determine an infection probability,and generate control decisions for the airside HVAC equipment using thedynamic infectious quanta model and the infection probability. In someembodiments, the control decisions provide a desired level ofdisinfection. In some embodiments, the control decisions indicate anamount of the clean air to be provided to the one or more building zonesby the airside HVAC equipment. In some embodiments, the controller isconfigured to obtain a dynamic temperature model for the one or morebuilding zones and generate the control decisions using both the dynamicinfectious quanta model and the dynamic temperature model. Obtaining thedynamic temperature model and the dynamic infectious quanta model caninclude receiving one or both of the models as inputs, generating one orboth of the models, retrieving one or both of the models from a databaseor from a user device, or otherwise obtaining one or both of the modelsin any other manner.

Another implementation of the present disclosure is a heating,ventilation, or air conditioning system (HVAC) design and operationaltool for a HVAC system for a building. The HVAC design and operationaltool includes one or more processors and memory storing instructionsthat, when executed by the one or more processors, cause the one or moreprocessors to perform operations including obtaining a dynamictemperature model and a dynamic infectious quanta model for one or morebuilding zones, determining an infection probability, and performing aplurality of simulations for a plurality of different equipmentconfigurations using the dynamic temperature model, the dynamicinfectious quanta model, and the infection probability to generateresults. The operations include generating, using the results of theplurality of simulations, at least one of design including one or morerecommended design parameters data or operational data including one ormore recommended operational parameters for the HVAC system andinitiating an automated action using at least one of the design data orthe operational data. Obtaining the dynamic temperature model and thedynamic infectious quanta model can include receiving one or both of themodels as inputs, generating one or both of the models, retrieving oneor both of the models from a database or from a user device, orotherwise obtaining one or both of the models in any other manner.

In some embodiments, the operations further include determining adynamic humidity model for the one or more building zones and performingthe plurality of simulations using the dynamic humidity model togenerate the results.

In some embodiments, the one or more recommended design parametersindicate whether to include disinfection lighting for disinfection inthe HVAC system, whether to include an air filter for disinfection inthe HVAC system, and whether to use fresh air for disinfection in theHVAC system.

In some embodiments, the one or more recommended design parameterscomprise a recommended rating of an air filter for use in the HVACsystem.

In some embodiments, the automated action includes presenting at leastone of the design data or the operational data to a user via a userinterface.

In some embodiments, the plurality of simulations comprise at least twoof a first simulation in which the HVAC system includes disinfectionlighting but does not include an air filter for disinfection, a secondsimulation in which the HVAC system includes the air filter but does notinclude the disinfection lighting for disinfection, a third simulationin which the HVAC system includes both the disinfection lighting and theair filter for disinfection, and a fourth simulation in which the HVACsystem includes neither of the disinfection lighting nor the air filterfor disinfection.

In some embodiments, the operations further include generating aninfectious quanta constraint based on a user input indicating a desireda level of disinfection, performing at least one of the plurality ofsimulations subject to the infectious quanta constraint to generate anestimated cost of operating the HVAC system, and presenting theestimated cost of operating the HVAC system via a user interface.

In some embodiments, the operations further include using the results ofthe plurality of simulations to provide a user interface that indicatesa tradeoff between infection probability and at least one of energy costor energy consumption.

In some embodiments, the recommended operational parameters comprise arecommended control scheme for the HVAC system.

Another implementation of the present disclosure is a heating,ventilation, or air conditioning (HVAC) system design and operationaltool for a HVAC system for a building. The HVAC design and operationaltool includes one or more processors and memory storing instructionsthat, when executed by the one or more processors, cause the one or moreprocessors to perform operations including obtaining a dynamictemperature model and a dynamic infectious quanta model for one or morebuilding zones, determining an infection probability, performing asimulation using the dynamic temperature model, the dynamic infectiousquanta model, and the infection probability to generate resultsincluding a recommended equipment configuration of the HVAC system, andinitiating an automated action using on the results. Obtaining thedynamic temperature model and the dynamic infectious quanta model caninclude receiving one or both of the models as inputs, generating one orboth of the models, retrieving one or both of the models from a databaseor from a user device, or otherwise obtaining one or both of the modelsin any other manner.

In some embodiments, the operations further include obtaining a dynamichumidity model for the one or more building zones and performing thesimulation using the dynamic humidity model to generate the results.

In some embodiments, the recommended equipment configuration indicateswhether the HVAC system includes disinfection lighting for disinfection,whether the HVAC system includes a filter for disinfection, and whetherthe HVAC system uses fresh air for disinfection.

In some embodiments, the results comprise recommended equipmentspecifications indicating at least one of a recommended rating of an airfilter or a recommended rating of disinfection lighting fordisinfection.

In some embodiments, the automated action includes presenting theresults via a user interface.

In some embodiments, performing the simulation includes optimizing anobjective function indicating a cost of operating the HVAC system usingone or more potential equipment configurations to provide a desiredlevel of disinfection.

In some embodiments, the desired level of disinfection is auser-selected value.

In some embodiments, the operations further include generating aninfectious quanta constraint based on a user input indicating a desireda level of disinfection, performing the simulation subject to theinfectious quanta constraint to generate an estimated cost of operatingthe HVAC system, and presenting the estimated cost of operating the HVACsystem via a user interface.

In some embodiments, the user input indicates a tradeoff between thedesired level of disinfection and energy cost, the energy costcomprising at least one of an estimated energy consumption of the HVACsystem or an estimated monetary cost of the energy consumption of theHVAC system.

Another implementation of the present disclosure is a method forproviding design and operating recommendations for a heating,ventilation, or air conditioning (HVAC) system to achieve a desiredlevel of infection control in a building. The method includes obtaininga dynamic temperature model and a dynamic infectious quanta model forone or more building zones, determining an infection probability, andusing the dynamic temperature model, the dynamic infectious quantamodel, and the infection probability to generate at least one of designrecommendations or operating recommendations to achieve the desiredlevel of infection control. The method further includes operating adisplay to provide the design recommendations or the operatingrecommendations to a user, each of the design recommendations or theoperating recommendations including an associated cost. Obtaining thedynamic temperature model and the dynamic infectious quanta model caninclude receiving one or both of the models as inputs, generating one orboth of the models, retrieving one or both of the models from a databaseor from a user device, or otherwise obtaining one or both of the modelsin any other manner.

In some embodiments, the design recommendations or the operatingrecommendations include at least one of a recommended equipmentconfiguration of the HVAC system, recommended equipment specificationsof the HVAC system, a recommended filter rating of a filter of the HVACsystem, a recommended model of equipment of the HVAC system, or arecommended control scheme for the HVAC system.

Those skilled in the art will appreciate that the summary isillustrative only and is not intended to be in any way limiting. Otheraspects, inventive features, and advantages of the devices and/orprocesses described herein, as defined solely by the claims, will becomeapparent in the detailed description set forth herein and taken inconjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a drawing of a building equipped with a HVAC system, accordingto some embodiments.

FIG. 2 is a block diagram of an airside system which can be implementedin the building of FIG. 1, according to some embodiments.

FIG. 3 is a block diagram of an HVAC system including a controllerconfigured to operate an air-handling unit (AHU) of the HVAC system ofFIG. 1, according to some embodiments.

FIG. 4 is a block diagram illustrating the controller of FIG. 3 ingreater detail, showing operations performed when the controller is usedin an on-line mode or real-time implementation for making controldecisions to minimize energy consumption of the HVAC system and providesufficient disinfection, according to some embodiments.

FIG. 5 is a block diagram illustrating the controller of FIG. 3 ingreater detail, showing operations performed when the controller is usedin an off-line or planning mode for making design suggestions tominimize energy consumption of the HVAC system and provide sufficientdisinfection, according to some embodiments.

FIG. 6 is a flow diagram of a process which can be performed by thecontroller of FIG. 3 for determining control decisions for an HVACsystem to minimize energy consumption and provide sufficientdisinfection, according to some embodiments.

FIG. 7 is a flow diagram of a process which can be performed by thecontroller of FIG. 3 for determining design suggestions for an HVACsystem to minimize energy consumption and provide sufficientdisinfection, according to some embodiments.

FIG. 8 is a graph of various design suggestions or information that canbe provided by the controller of FIG. 3, according to some embodiments.

FIG. 9 is a drawing of a user interface that can be used to specifybuilding options and disinfection options and provide simulationresults, according to some embodiments.

FIG. 10 is a graph illustrating a technique which can be used by thecontroller of FIG. 3 to estimate a Pareto front of a tradeoff curve forrelative energy cost vs. infection probability, according to someembodiments.

DETAILED DESCRIPTION Overview

Referring generally to the FIGURES, systems and methods for minimizingenergy consumption of an HVAC system while maintaining a desired levelof disinfection are shown. The system may include an AHU that servesmultiple zones, a controller, one or more UV lights that disinfect airbefore it is provided from the AHU to the zones, and/or a filter that isconfigured to filter air to provide additional disinfection for the airbefore it is provided to the zones. In some embodiments, the system alsoincludes one or more zone sensors (e.g., temperature and/or humiditysensors, etc.) and one or more ambient or outdoor sensors (e.g., outdoortemperature and/or outdoor humidity sensors, etc.).

The controller uses a model-based design and optimization framework tointegrate building disinfection control with existing temperatureregulation in building HVAC systems. The controller uses the Wells-Rileyequation to transform a required upper limit of infection probabilityinto constraints on indoor concentration of infectious particles,according to some embodiments. In some embodiments, the controller usesa dynamic model for infectious agent concentration to impose theseconstraints on an optimization problem similar to temperature andhumidity constraints. By modeling effects of various types of optionalinfection control equipment (e.g., UV lights and/or filters), thecontroller may utilize a combination of fresh-air ventilation and directfiltration/disinfection to achieve desired infection constraints. Insome embodiments, the controller can use this composite model foroptimal design (e.g., in an off-line implementation of the controller)to determine which additional disinfection strategies are desirable,cost effective, or necessary. The controller can also be used foron-line control to determine control decisions for various controllableequipment (e.g., dampers of the AHU) in real-time to minimize energyconsumption or energy costs of the HVAC system while meetingtemperature, humidity, and infectious quanta concentration constraints.

The systems and methods described herein treat infection control as anintegral part of building HVAC operation rather than a short term orindependent control objective, according to some embodiments. While itmay be possible to achieve disinfection by the addition of UV lights andfilters running at full capacity, such a strategy may be costly andconsume excessive amounts of energy. However, the systems and methodsdescribed herein couple both objectives (disinfection control andminimal energy consumption) to assess optimal design and operationaldecisions on a case-by-case basis also taking into account climate,energy and disinfection goals of particular buildings.

The controller can be implemented in an off-line mode as a design tool.With the emergence of various strategies for building disinfection,building designers and operators now have a wide array of options forretrofitting a building to reduce the spread of infectious diseases tobuilding occupants. This is typically accomplished by lowering theconcentration of infectious particles in the air space, which can beaccomplished by killing the microbes via UV radiation, trapping them viafiltration, or simply forcing them out of the building via fresh-airventilation. While any one of these strategies individually can providedesired levels of disinfection, it may do so at unnecessarily high costor with negative consequences for thermal comfort of building occupants.Thus, to help evaluate the tradeoff and potential synergies between thevarious disinfection options, the model-based design tool can estimateannualized capital and energy costs for a given set of disinfectionequipment. For a given AHU, this includes dynamic models fortemperature, humidity, and infectious particle concentration, and itemploys the Wells-Riley infection equation to enforce constraints onmaximum occupant infection probability. By being able to quicklysimulate a variety of simulation instances, the controller (whenoperating as the design tool in the off-line mode) can present buildingdesigners with the tradeoff between cost and disinfection, allowing themto make informed decisions about retrofit.

A key feature of the design tool is that it shows to what extent theinherent flexibility of the existing HVAC system can be used to providedisinfection. In particular, in months when infectivity is of biggestconcern, a presence of free cooling from fresh outdoor air means thatthe energy landscape is relatively flat regardless of how the controllerdetermines to operate the HVAC system. Thus, the controller couldpotentially increase fresh-air intake significantly to providesufficient disinfection without UV or advanced filtration whileincurring only a small energy penalty. The design tool can provideestimates to customers to allow them to make informed decisions aboutwhat additional disinfection equipment (if any) to install and thenprovide the modified control systems needed to implement the desiredinfection control.

The controller can also be implemented in an on-line mode as a real-timecontroller. Although equipment like UV lamps and advanced filtration canbe installed in buildings to mitigate the spread of infectious diseases,it is often unclear how to best operate that equipment to achievedesired disinfection goals in a cost-effective manner. A common strategyis to take the robust approach of opting for the highest-efficiencyfilters and running UV lamps constantly. While this strategy will indeedreduce infection probability to its lowest possible value, it is likelyto do so at exorbitant cost due to the constant energy penalties of bothstrategies. Building managers may potentially choose to completelydisable filters and UV lamps to conserve energy consumption. Thus, thebuilding may end up in a worst-of-both-words situation where thebuilding manager has paid for disinfection equipment but the zones areno longer receiving any disinfection. To remove this burden frombuilding operators, the controller can automate infection control byintegrating disinfection control (e.g., based on the Wells-Rileyequation) in a model based control scheme. In this way, the controllercan simultaneously achieve thermal comfort and provide adequatedisinfection at the lowest possible cost given currently availableequipment.

Advantageously, the control strategy can optimize in real time theenergy and disinfection tradeoffs of all possible control variables.Specifically, the controller may choose to raise fresh-air intakefraction even though it incurs a slight energy penalty because it allowsa significant reduction of infectious particle concentrations whilestill maintaining comfortable temperatures. Thus, in some climates itmay be possible to provide disinfection without additional equipment,but this strategy is only possible if the existing controlinfrastructure can be guided or constrained so as to provide desireddisinfection. Alternatively, in buildings that have chosen to add UVlamps and/or filtration, the controller can find the optimal combinationof techniques to achieve desired control objectives at the lowestpossible cost. In addition, because the constraint on infectionprobability is configurable, the controller can empower buildingoperators to make their own choices regarding disinfection and energyuse (e.g. opting for a loose constraint in the summer when disease israre and energy use is intensive, while transitioning to a tightconstraint in winter when disease is prevalent and energy less of aconcern). Advantageously, the controller can provide integrated comfort,disinfection, and energy management to customers to achieve betteroutcomes in all three areas compared to other narrow and individualsolutions.

In some embodiments, the models used to predict temperature, humidity,and/or infectious quanta are dynamic models. The term “dynamic model”and variants thereof (e.g., dynamic temperature model, dynamic humiditymodel, dynamic infectious quanta model, etc.) are used throughout thepresent disclosure to refer to any type of model that predicts the valueof a quantity (e.g., temperature, humidity, infectious quanta) atvarious points in time as a function of zero or more input variables. Adynamic model may be “dynamic” as a result of the input variableschanging over time even if the model itself does not change. Forexample, a steady-state model that uses ambient temperature or any othervariable that changes over time as an input may be considered a dynamicmodel. Dynamic models may also include models that vary over time. Forexample, models that are retrained periodically, configured to adapt tochanging conditions over time, and/or configured to use differentrelationships between input variables and predicted outputs (e.g., afirst set of relationships for winter months and a second set ofrelationships for summer months) may also be considered dynamic models.Dynamic models may also include ordinary differential equation (ODE)models or other types of models having input variables that change overtime and/or input variables that represent the rate of change of avariable.

Building and HVAC System

Referring now to FIG. 1, a perspective view of a building 10 is shown.Building 10 can be served by a building management system (BMS). A BMSis, in general, a system of devices configured to control, monitor, andmanage equipment in or around a building or building area. A BMS caninclude, for example, a HVAC system, a security system, a lightingsystem, a fire alerting system, any other system that is capable ofmanaging building functions or devices, or any combination thereof. Anexample of a BMS which can be used to monitor and control building 10 isdescribed in U.S. patent application Ser. No. 14/717,593 filed May 20,2015, the entire disclosure of which is incorporated by referenceherein.

The BMS that serves building 10 may include a HVAC system 100. HVACsystem 100 can include a plurality of HVAC devices (e.g., heaters,chillers, air handling units, pumps, fans, thermal energy storage, etc.)configured to provide heating, cooling, ventilation, or other servicesfor building 10. For example, HVAC system 100 is shown to include awaterside system 120 and an airside system 130. Waterside system 120 mayprovide a heated or chilled fluid to an air handling unit of airsidesystem 130. Airside system 130 may use the heated or chilled fluid toheat or cool an airflow provided to building 10. In some embodiments,waterside system 120 can be replaced with or supplemented by a centralplant or central energy facility (described in greater detail withreference to FIG. 2). An example of an airside system which can be usedin HVAC system 100 is described in greater detail with reference to FIG.2.

HVAC system 100 is shown to include a chiller 102, a boiler 104, and arooftop air handling unit (AHU) 106. Waterside system 120 may use boiler104 and chiller 102 to heat or cool a working fluid (e.g., water,glycol, etc.) and may circulate the working fluid to AHU 106. In variousembodiments, the HVAC devices of waterside system 120 can be located inor around building 10 (as shown in FIG. 1) or at an offsite locationsuch as a central plant (e.g., a chiller plant, a steam plant, a heatplant, etc.). The working fluid can be heated in boiler 104 or cooled inchiller 102, depending on whether heating or cooling is required inbuilding 10. Boiler 104 may add heat to the circulated fluid, forexample, by burning a combustible material (e.g., natural gas) or usingan electric heating element. Chiller 102 may place the circulated fluidin a heat exchange relationship with another fluid (e.g., a refrigerant)in a heat exchanger (e.g., an evaporator) to absorb heat from thecirculated fluid. The working fluid from chiller 102 and/or boiler 104can be transported to AHU 106 via piping 108.

AHU 106 may place the working fluid in a heat exchange relationship withan airflow passing through AHU 106 (e.g., via one or more stages ofcooling coils and/or heating coils). The airflow can be, for example,outside air, return air from within building 10, or a combination ofboth. AHU 106 may transfer heat between the airflow and the workingfluid to provide heating or cooling for the airflow. For example, AHU106 can include one or more fans or blowers configured to pass theairflow over or through a heat exchanger containing the working fluid.The working fluid may then return to chiller 102 or boiler 104 viapiping 110.

Airside system 130 may deliver the airflow supplied by AHU 106 (i.e.,the supply airflow) to building 10 via air supply ducts 112 and mayprovide return air from building 10 to AHU 106 via air return ducts 114.In some embodiments, airside system 130 includes multiple variable airvolume (VAV) units 116. For example, airside system 130 is shown toinclude a separate VAV unit 116 on each floor or zone of building 10.VAV units 116 can include dampers or other flow control elements thatcan be operated to control an amount of the supply airflow provided toindividual zones of building 10. In other embodiments, airside system130 delivers the supply airflow into one or more zones of building 10(e.g., via supply ducts 112) without using intermediate VAV units 116 orother flow control elements. AHU 106 can include various sensors (e.g.,temperature sensors, pressure sensors, etc.) configured to measureattributes of the supply airflow. AHU 106 may receive input from sensorslocated within AHU 106 and/or within the building zone and may adjustthe flow rate, temperature, or other attributes of the supply airflowthrough AHU 106 to achieve setpoint conditions for the building zone.

Airside System

Referring now to FIG. 2, a block diagram of an airside system 200 isshown, according to some embodiments. In various embodiments, airsidesystem 200 may supplement or replace airside system 130 in HVAC system100 or can be implemented separate from HVAC system 100. Whenimplemented in HVAC system 100, airside system 200 can include a subsetof the HVAC devices in HVAC system 100 (e.g., AHU 106, VAV units 116,ducts 112-114, fans, dampers, etc.) and can be located in or aroundbuilding 10. Airside system 200 may operate to heat, cool, humidify,dehumidify, filter, and/or disinfect an airflow provided to building 10in some embodiments.

Airside system 200 is shown to include an economizer-type air handlingunit (AHU) 202. Economizer-type AHUs vary the amount of outside air andreturn air used by the air handling unit for heating or cooling. Forexample, AHU 202 may receive return air 204 from building zone 206 viareturn air duct 208 and may deliver supply air 210 to building zone 206via supply air duct 212. In some embodiments, AHU 202 is a rooftop unitlocated on the roof of building 10 (e.g., AHU 106 as shown in FIG. 1) orotherwise positioned to receive both return air 204 and outside air 214.AHU 202 can be configured to operate exhaust air damper 216, mixingdamper 218, and outside air damper 220 to control an amount of outsideair 214 and return air 204 that combine to form supply air 210. Anyreturn air 204 that does not pass through mixing damper 218 can beexhausted from AHU 202 through exhaust damper 216 as exhaust air 222.

Each of dampers 216-220 can be operated by an actuator. For example,exhaust air damper 216 can be operated by actuator 224, mixing damper218 can be operated by actuator 226, and outside air damper 220 can beoperated by actuator 228. Actuators 224-228 may communicate with an AHUcontroller 230 via a communications link 232. Actuators 224-228 mayreceive control signals from AHU controller 230 and may provide feedbacksignals to AHU controller 230. Feedback signals can include, forexample, an indication of a current actuator or damper position, anamount of torque or force exerted by the actuator, diagnosticinformation (e.g., results of diagnostic tests performed by actuators224-228), status information, commissioning information, configurationsettings, calibration data, and/or other types of information or datathat can be collected, stored, or used by actuators 224-228. AHUcontroller 230 can be an economizer controller configured to use one ormore control algorithms (e.g., state-based algorithms, extremum seekingcontrol (ESC) algorithms, proportional-integral (PI) control algorithms,proportional-integral-derivative (PID) control algorithms, modelpredictive control (MPC) algorithms, feedback control algorithms, etc.)to control actuators 224-228.

Still referring to FIG. 2, AHU 202 is shown to include a cooling coil234, a heating coil 236, and a fan 238 positioned within supply air duct212. Fan 238 can be configured to force supply air 210 through coolingcoil 234 and/or heating coil 236 and provide supply air 210 to buildingzone 206. AHU controller 230 may communicate with fan 238 viacommunications link 240 to control a flow rate of supply air 210. Insome embodiments, AHU controller 230 controls an amount of heating orcooling applied to supply air 210 by modulating a speed of fan 238. Insome embodiments, AHU 202 includes one or more air filters (e.g., filter308) and/or one or more ultraviolet (UV) lights (e.g., UV lights 306) asdescribed in greater detail with reference to FIG. 3. AHU controller 230can be configured to control the UV lights and route the airflow throughthe air filters to disinfect the airflow as described in greater detailbelow.

Cooling coil 234 may receive a chilled fluid from central plant 200(e.g., from cold water loop 216) via piping 242 and may return thechilled fluid to central plant 200 via piping 244. Valve 246 can bepositioned along piping 242 or piping 244 to control a flow rate of thechilled fluid through cooling coil 234. In some embodiments, coolingcoil 234 includes multiple stages of cooling coils that can beindependently activated and deactivated (e.g., by AHU controller 230, byBMS controller 266, etc.) to modulate an amount of cooling applied tosupply air 210.

Heating coil 236 may receive a heated fluid from central plant 200(e.g., from hot water loop 214) via piping 248 and may return the heatedfluid to central plant 200 via piping 250. Valve 252 can be positionedalong piping 248 or piping 250 to control a flow rate of the heatedfluid through heating coil 236. In some embodiments, heating coil 236includes multiple stages of heating coils that can be independentlyactivated and deactivated (e.g., by AHU controller 230, by BMScontroller 266, etc.) to modulate an amount of heating applied to supplyair 210.

Each of valves 246 and 252 can be controlled by an actuator. Forexample, valve 246 can be controlled by actuator 254 and valve 252 canbe controlled by actuator 256. Actuators 254-256 may communicate withAHU controller 230 via communications links 258-260. Actuators 254-256may receive control signals from AHU controller 230 and may providefeedback signals to controller 230. In some embodiments, AHU controller230 receives a measurement of the supply air temperature from atemperature sensor 262 positioned in supply air duct 212 (e.g.,downstream of cooling coil 334 and/or heating coil 236). AHU controller230 may also receive a measurement of the temperature of building zone206 from a temperature sensor 264 located in building zone 206.

In some embodiments, AHU controller 230 operates valves 246 and 252 viaactuators 254-256 to modulate an amount of heating or cooling providedto supply air 210 (e.g., to achieve a setpoint temperature for supplyair 210 or to maintain the temperature of supply air 210 within asetpoint temperature range). The positions of valves 246 and 252 affectthe amount of heating or cooling provided to supply air 210 by coolingcoil 234 or heating coil 236 and may correlate with the amount of energyconsumed to achieve a desired supply air temperature. AHU 230 maycontrol the temperature of supply air 210 and/or building zone 206 byactivating or deactivating coils 234-236, adjusting a speed of fan 238,or a combination of both.

Still referring to FIG. 2, airside system 200 is shown to include abuilding management system (BMS) controller 266 and a client device 268.BMS controller 266 can include one or more computer systems (e.g.,servers, supervisory controllers, subsystem controllers, etc.) thatserve as system level controllers, application or data servers, headnodes, or master controllers for airside system 200, central plant 200,HVAC system 100, and/or other controllable systems that serve building10. BMS controller 266 may communicate with multiple downstream buildingsystems or subsystems (e.g., HVAC system 100, a security system, alighting system, central plant 200, etc.) via a communications link 270according to like or disparate protocols (e.g., LON, BACnet, etc.). Invarious embodiments, AHU controller 230 and BMS controller 266 can beseparate (as shown in FIG. 2) or integrated. In an integratedimplementation, AHU controller 230 can be a software module configuredfor execution by a processor of BMS controller 266.

In some embodiments, AHU controller 230 receives information from BMScontroller 266 (e.g., commands, setpoints, operating boundaries, etc.)and provides information to BMS controller 266 (e.g., temperaturemeasurements, valve or actuator positions, operating statuses,diagnostics, etc.). For example, AHU controller 230 may provide BMScontroller 266 with temperature measurements from temperature sensors262-264, equipment on/off states, equipment operating capacities, and/orany other information that can be used by BMS controller 266 to monitoror control a variable state or condition within building zone 206.

Client device 268 can include one or more human-machine interfaces orclient interfaces (e.g., graphical user interfaces, reportinginterfaces, text-based computer interfaces, client-facing web services,web servers that provide pages to web clients, etc.) for controlling,viewing, or otherwise interacting with HVAC system 100, its subsystems,and/or devices. Client device 268 can be a computer workstation, aclient terminal, a remote or local interface, or any other type of userinterface device. Client device 268 can be a stationary terminal or amobile device. For example, client device 268 can be a desktop computer,a computer server with a user interface, a laptop computer, a tablet, asmartphone, a PDA, or any other type of mobile or non-mobile device.Client device 268 may communicate with BMS controller 266 and/or AHUcontroller 230 via communications link 272.

HVAC System with Building Infection Control

Overview

Referring particularly to FIG. 3, a HVAC system 300 that is configuredto provide disinfection for various zones of a building (e.g., building10) is shown, according to some embodiments. HVAC system 300 can includean air handling unit (AHU) 304 (e.g., AHU 230, AHU 202, etc.) that canprovide conditioned air (e.g., cooled air, supply air 210, etc.) tovarious building zones 206. The AHU 304 may draw air from the zones 206in combination with drawing air from outside (e.g., outside air 214) toprovide conditioned or clean air to zones 206. The HVAC system 1400includes a controller 310 (e.g., AHU controller 230) that is configuredto determine a fraction x of outdoor air to recirculated air that theAHU 304 should use to provide a desired amount of disinfection tobuilding zones 206. In some embodiments, controller 310 can generatecontrol signals for various dampers of AHU 304 so that AHU 304 operatesto provide the conditioned air to building zones 206 using the fractionx.

The HVAC system 300 can also include ultraviolet (UV) lights 306 thatare configured to provide UV light to the conditioned air before it isprovided to building zones 206. The UV lights 306 can providedisinfection as determined by controller 310 and/or based on useroperating preferences. For example, the controller 310 can determinecontrol signals for UV lights 306 in combination with the fraction x ofoutdoor air to provide a desired amount of disinfection and satisfy aninfection probability constraint. Although UV lights 306 are referred tothroughout the present disclosure, the systems and methods describedherein can use any type of disinfection lighting using any frequency,wavelength, or luminosity of light effective for disinfection. It shouldbe understood that UV lights 306 (and any references to UV lights 306throughout the present disclosure) can be replaced with disinfectionlighting of any type without departing from the teachings of the presentdisclosure.

The HVAC system 300 can also include one or more filters 308 orfiltration devices (e.g., air purifiers). In some embodiments, thefilters 308 are configured to filter the conditioned air or recirculatedair before it is provided to building zones 206 to provide a certainamount of disinfection. In this way, controller 310 can perform anoptimization in real-time or as a planning tool to determine controlsignals for AHU 304 (e.g., the fraction x) and control signals for UVlights 306 (e.g., on/off commands) to provide disinfection for buildingzones 206 and reduce a probability of infection of individuals that areoccupying building zones 206. Controller 310 can also function as adesign tool that is configured to determine suggestions for buildingmanagers regarding benefits of installing or using filters 308, and/orspecific benefits that may arise from using or installing a particulartype or size of filter. Controller 310 can thereby facilitate informeddesign decisions to maintain sterilization of air that is provided tobuilding zones 206 and reduce a likelihood of infection or spreading ofinfectious matter.

Wells-Riley Airborne Transmission

The systems and methods described herein may use an infectionprobability constraint in various optimizations (e.g., in on-line orreal-time optimizations or in off-line optimizations) to facilitatereducing infection probability among residents or occupants of spacesthat the HVAC system serves. The infection probability constraint can bebased on a steady-state Wells-Riley equation for a probability ofairborne transmission of an infectious agent given by:

${P:} = {\frac{D}{S} = {1 - {\exp\left( {- \frac{Ipqt}{Q}} \right)}}}$

where P is a probability that an individual becomes infected (e.g., in azone, space, room, environment, etc.), D is a number of infectedindividuals (e.g., in the zone, space, room, environment, etc.), S is atotal number of susceptible individuals (e.g., in the zone, space, room,environment, etc.), I is a number of infectious individuals (e.g., inthe zone, space, room, environment, etc.), q is a disease quantageneration rate (e.g., with units of 1/sec), p is a volumetric breathrate of one individual (e.g., in m³/sec), t is a total exposure time(e.g., in seconds), and Q is an outdoor ventilation rate (e.g., inm³/sec). For example, Q may be a volumetric flow rate of fresh outdoorair that is provided to the building zones 206 by AHU 304.

When the Wells-Riley equation is implemented by controller 310 asdescribed herein, controller 310 may use the Wells-Riley equation (or adynamic version of the Wells-Riley equation) to determine an actual orcurrent probability of infection P and operate the HVAC system 200 tomaintain the actual probability of infection P below (or drive theactual probability of infection below) a constraint or maximum allowablevalue. The constraint value (e.g., P_(max)) may be a constant value, ormay be adjustable by a user (e.g., a user-set value). For example, theuser may set the constraint value of the probability of infection to amaximum desired probability of infection (e.g., either for on-lineimplementation of controller 310 to maintain the probability ofinfection below the maximum desired probability, or for an off-lineimplementation/simulation performed by controller 310 to determinevarious design parameters for HVAC system 200 such as filter size), ormay select from various predetermined values (e.g., 3-5 differentchoices of the maximum desired probability of infection).

In some embodiments, the number of infectious individuals I can bedetermined by controller 310 based on data from the Centers for Diseaseand Control Prevention or a similar data source. The value of I may betypically set equal to 1 but may vary as a function of occupancy ofbuilding zones 206.

The disease quanta generation rate q may be a function of the infectiousagent. For example, more infectious diseases may have a higher value ofq, while less infectious diseases may have a lower value of q. Forexample, the value of q for COVID-19 may be 30-300 (e.g., 100).

The value of the volumetric breath rate p may be based on a type ofbuilding space 206. For example, the volumetric breath rate p may behigher if the building zone 206 is a gym as opposed to an officesetting. In general, an expected level of occupant activity maydetermine the value of the volumetric breath rate p.

A difference between D (the number of infected individuals) and I (thenumber of infectious individuals) is that D is a number of individualswho are infected (e.g., infected with a disease), while I is a number ofpeople that are infected and are actively contagious (e.g., individualsthat may spread the disease to other individuals or spread infectiousparticles when they exhale). The disease quanta generation rateindicates a number of infectious droplets that give a 63.2% chance ofinfecting an individual (e.g., 1−exp(−1)). For example, if an individualinhales k infectious particles, the probability that the individualbecomes infected (P) is given by

$1 - {\exp\left( {- \frac{k}{k_{0}}} \right)}$

where k is the number of infectious particles that the individual hasinhaled, and k₀ is a quantum of particles for a particular disease(e.g., a predefined value for different diseases). The quanta generationrate q is the rate at which quanta are generated (e.g., K/k₀) where K isthe rate of infectious particles exhaled by an infectious individual. Itshould be noted that values of the disease quanta generation rate q maybe back-calculated from epidemiological data or may be tabulated forwell-known diseases.

The Wells-Riley equation (shown above) is derived by assumingsteady-state concentrations for infectious particles in the air.Assuming a well-mixed space:

${V\frac{dN}{dt}} = {{Iq} - {NQ}}$

where V is a total air volume (e.g., in m³), N is a quantumconcentration in the air, I is the number of infectious individuals, qis the disease quanta generation rate, and Q is the outdoor ventilationrate. The term Iq is quanta production by infectious individuals (e.g.,as the individuals breathe out or exhale), and the term NQ is the quantaremoval rate due to ventilation (e.g., due to operation of AHU 304).

Assuming steady-state conditions, the steady state quantum concentrationin the air is expressed as:

$N_{ss} = \frac{Iq}{Q}$

according to some embodiments.

Therefore, if an individual inhales at an average rate of p (e.g., inm³/sec), over a period of length t the individual inhales a total volumept or N_(ss)ptk₀ infectious particles. Therefore, based on a probabilitymodel used to define the quanta, the infectious probability is given by:

$P = {{1 - {\exp\left( {- \frac{k}{k_{0}}} \right)}} = {{1 - {\exp\left( {{- N_{SS}}{pt}} \right)}} = {1 - {\exp\left( {- \frac{Iqpt}{Q}} \right)}}}}$

where P is the probability that an individual becomes infected, k is thenumber of infectious particles that the individual has inhaled, and k₀is the quantum of particles for the particular disease.

Carbon Dioxide for Infectious Particles Proxy

While the above equations may rely on in-air infectious quantaconcentration, measuring in-air infectious quanta concentration may bedifficult. However, carbon dioxide (CO2) is a readily-measureableparameter that can be a proxy species, measured by zone sensors 312. Insome embodiments, a concentration of CO2 in the zones 206 may bedirectly related to a concentration of the infectious quanta.

A quantity ϕ that defines a ratio of an infected particle concentrationin the building air to the infected particle concentration in theexhaled breath of an infectious individual is defined:

${\phi:} = \frac{pN}{q}$

where p is the volumetric breath rate for an individual, N is thequantum concentration in the air, and q is the disease quanta generationrate. Deriving the above equation with respect to time yields:

$\frac{d\phi}{dt} = {{\frac{p}{q}\left( \frac{dN}{dt} \right)} = {\frac{Ip}{V} - {\phi\left( \frac{Q}{V} \right)}}}$

where p is the volumetric breath rate for the individual, q is diseasequanta generation rate, N is the quantum concentration in the air, t istime, I is the number of infectious individuals, V is the total airvolume, ϕ is the ratio, and Q is the outdoor ventilation rate. Since itcan be difficult to measure the ratio ϕ of the air, CO2 can be used as aproxy species.

Humans release CO2 when exhaling, which is ultimately transferred to theambient via ventilation of an HVAC system. Therefore, the differencebetween CO2 particles and infectious particles is that all individuals(and not only the infectious population) release CO2 and that theoutdoor air CO2 concentration is non-zero. However, it may be assumedthat the ambient CO2 concentration is constant with respect to time,which implies that a new quantity C can be defined as the net indoor CO2concentration (e.g., the indoor concentration minus the outdoorconcentration). With this assumption, the following differentialequation can be derived:

${V\frac{dC}{dt}} = {{Spc} - {QC}}$

where V is the total air volume (e.g., in m³), C is the net indoor CO2concentration, t is time, S is the total number of susceptibleindividuals (e.g., in building zone 206, or a modeled space, or all ofbuilding zones 206, or building 10), p is the volumetric breath rate forone individual, c is the net concentration of exhaled CO2, and Q is theoutdoor ventilation rate. This equation assumes that the only way toremove infectious particles is with fresh air ventilation (e.g., byoperating AHU 304 to draw outdoor air and use the outdoor air withrecirculated air). A new quantity ψ can be defined that gives the ratioof net CO2 concentration in the building air to net CO2 concentration inthe exhaled air:

$\psi = \frac{C}{c}$

where ψ is the ratio, C is the net indoor CO2 concentration, and c isthe net concentration of exhaled CO2.

Deriving the ratio with respect to time yields:

$\frac{d\psi}{dt} = {{\frac{1}{c}\left( \frac{dC}{dt} \right)} = {\frac{Sp}{V} - {\psi\left( \frac{Q}{V} \right)}}}$

according to some embodiments.

Combining the above equation with the quantity ϕ, it can be derivedthat:

${\frac{d}{dt}{\log\left( \frac{\phi}{\psi} \right)}} = {{{\frac{1}{\phi}\left( \frac{d\phi}{dt} \right)} - {\frac{1}{\psi}\left( \frac{d\psi}{dt} \right)}} = {\frac{p}{V}\left( {\frac{I}{\phi} - \frac{S}{\psi}} \right)}}$

according to some embodiments. Assuming that the initial conditionsatisfies:

${\phi(0)} = {\frac{1}{S}{\psi(0)}}$

it can be determined that the right-hand side of the

$\frac{d}{dt}{\log\left( \frac{\phi}{\psi} \right)}$

equation becomes zero. This implies that the term log

$\left( \frac{\phi}{\psi} \right)$

and therefore

$\frac{\phi}{\psi}$

is a constant. Therefore, ϕ/ψ is constant for all times t and not merelyinitial conditions when t=0.

The

$\frac{d}{dt}{\log\left( \frac{\phi}{\psi} \right)}$

relationship only holds true when fresh outdoor air is used as the onlydisinfection mechanism. However, in many cases HVAC system 200 mayinclude one or more filters 308, and UV lights 306 that can be operatedto provide disinfection for building zones 206. If additional infectionmitigation strategies are used, the ventilation rate may instead by aneffective ventilation rate for infectious quanta that is different thanthat of the CO2. Additionally, the only way for the initial conditionsϕ(0) and ψ(0) to be in proportion is for both to be zero. Thisassumption can be reasonable if HVAC system 200 operates over aprolonged time period (such as overnight, when the concentrations havesufficient time to reach equilibrium zero values). However, ventilationis often partially or completely disabled overnight and therefore thetwo quantities ϕ and ψ are not related. However, CO2 concentration canbe measured to determine common model parameters (e.g., for the overallsystem volume V) without being used to estimate current infectiousparticle concentrations. If fresh outdoor air ventilation is the onlymechanism for disinfection of zones 206, and the HVAC system 200 is runso that the concentrations reach equilibrium, CO2 concentration can bemeasured and used to estimate current infectious particleconcentrations.

Dynamic Extension and Infection Probability Constraints

Referring still to FIG. 3, it may be desirable to model the infectiousquanta concentration N of building zones 206 as a dynamic parameterrather than assuming N is equal to the steady state N_(SS) value. Forexample, if infectious individuals enter building zones 206, leavebuilding zones 206, etc., the infectious quanta concentration N maychange over time. This can also be due to the fact that the effectivefresh air ventilation rate (which includes outdoor air intake as well asfiltration or UV disinfection that affects the infectious agentconcentration in the supply air that is provided by AHU 304 to zones206) can vary as HVAC system 200 operates.

Therefore, assuming that the infectious quanta concentration N(t) is atime-varying quantity, for a given time period t∈[0, T], an individualbreathes in:

k _([0,T])=∫₀ ^(T) pk ₀ N(t)dt

where k_([0,7]) is the number of infectious particles that an individualinhales over the given time period [0, T], p is the volumetric breathrate of one individual, k₀ is the quantum of particles for a particulardisease, and N(t) is the time-varying quantum concentration of theinfectious particle in the air.

Since

${P = {1 - {\exp\left( {- \frac{k}{k_{0}}} \right)}}},$

the above equation can be rearranged and substitution yields:

${- {\log\left( {1 - P_{\lbrack{0,T}\rbrack}} \right)}} = {{\int_{0}^{T}{{{pN}(t)}{dt}}} \approx {\Delta{\sum\limits_{t}{pN}_{t}}}}$

according to some embodiments.

Assuming an upper boundary P_([0,T]) ^(max) on acceptable or desirableinfection probability, a constraint is defined as:

${\frac{\Delta}{T}{\sum\limits_{t}N_{t}}} \leq {{- \frac{1}{pT}}{\log\left( {1 - P_{\lbrack{0,T}\rbrack}} \right)}}$

according to some embodiments. The constraint can define a fixed upperboundary on an average value of N_(t) over the given time interval.

Control Formulation

Referring particularly to FIG. 4, controller 310 is shown in greaterdetail, according to some embodiments. Controller 310 is configured togenerate control signals for any of UV lights 306, filter 308, and/orAHU 304. AHU 304 operates to draw outdoor air and/or recirculated air(e.g., from zones 206) to output conditioned (e.g., cooled) air. Theconditioned air may be filtered by passing through filter 308 (e.g.,which may include fans to draw the air through the filter 308) to outputfiltered air. The filtered air and/or the conditioned air can bedisinfected through operation of UV lights 306. The AHU 304, filter 308,and UV lights 306 can operate in unison to provide supply air to zones206.

Controller 310 includes a processing circuit 402 including a processor404 and memory 406. Processing circuit 402 can be communicably connectedwith a communications interface of controller 310 such that processingcircuit 402 and the various components thereof can send and receive datavia the communications interface. Processor 404 can be implemented as ageneral purpose processor, an application specific integrated circuit(ASIC), one or more field programmable gate arrays (FPGAs), a group ofprocessing components, or other suitable electronic processingcomponents.

Memory 406 (e.g., memory, memory unit, storage device, etc.) can includeone or more devices (e.g., RAM, ROM, Flash memory, hard disk storage,etc.) for storing data and/or computer code for completing orfacilitating the various processes, layers and modules described in thepresent application. Memory 406 can be or include volatile memory ornon-volatile memory. Memory 406 can include database components, objectcode components, script components, or any other type of informationstructure for supporting the various activities and informationstructures described in the present application. According to someembodiments, memory 406 is communicably connected to processor 404 viaprocessing circuit 402 and includes computer code for executing (e.g.,by processing circuit 402 and/or processor 404) one or more processesdescribed herein.

In some embodiments, controller 310 is implemented within a singlecomputer (e.g., one server, one housing, etc.). In various otherembodiments controller 310 can be distributed across multiple servers orcomputers (e.g., that can exist in distributed locations).

Memory 406 can include a constraint generator 410, a model manager 416,a sensor manager 414, an optimization manager 412, and a control signalgenerator 408. Sensor manager 414 can be configured to obtain zonesensor data from zone sensors 312 and/or ambient sensor data fromambient sensors 314 (e.g., environmental conditions, outdoortemperature, outdoor humidity, etc.) and distribute required sensor datato the various components of memory 406 thereof. Constraint generator410 is configured to generate one or more constraints for anoptimization problem (e.g., an infection probability constraint) andprovide the constraints to optimization manager 412. Model manager 416can be configured to generate dynamic models (e.g., individual orzone-by-zone dynamic models, aggregate models, etc.) and provide thedynamic models to optimization manager 412. Optimization manager 412 canbe configured to use the constraints provided by constraint generator410 and the dynamic models provided by model manager 416 to formulate anoptimization problem. Optimization manager 412 can also define anobjective function for the optimization problem, and minimize oroptimize the objective function subject to the one or more constraintsand the dynamic models. The objective function may be a function thatindicates an amount of energy consumption, energy consumption costs,carbon footprint, or any other optimization goals over a time intervalor time horizon (e.g., a future time horizon) as a function of variouscontrol decisions. Optimization manager 412 can output optimizationsresults to control signal generator 408. Control signal generator 408can generate control signals based on the optimization results andprovide the control signals to any of AHU 304, filter 308, and/or UVlights 306.

Referring particularly to FIGS. 3 and 4, AHU 304 can be configured toserve multiple building zones 206. For example, AHU 304 can beconfigured to serve a collection of zones 206 that are numbered k=1, . .. , K. Each zone 206 can have a temperature, referred to as temperatureT_(k) (the temperature of the kth zone 206), a humidity ω_(k) (thehumidity of the kth zone 206), and an infectious quanta concentrationN_(k) (the infectious quanta concentration of the kth zone 206). Usingthis notation, the following dynamic models of individual zones 206 canbe derived:

${\rho\;{{cV}_{k}\left( \frac{{dT}_{k}}{dt} \right)}} = {{\rho\;{{cf}_{k}\left( {T_{0} - T_{k}} \right)}} + {Q_{k}\left( T_{k} \right)}}$${\rho{V_{k}\left( \frac{d\omega_{k}}{dt} \right)}} = {{\rho{f\left( {\omega_{0} - T_{0}} \right)}} + w_{k}}$${V_{k}\left( \frac{{dN}_{k}}{dt} \right)} = {{f_{k}\left( {N_{0} - N_{k}} \right)} + {I_{k}q}}$

where f_(k) is a volumetric flow of air into the kth zone, ρ is a massdensity of air (e.g., in kg per cubic meters), c is the heat capacity ofair (e.g., in kJ/kg·K), Q_(k)(⋅) is heat load on the kth zone 206 (whichmay depend on the temperature T_(k)), w_(k) is the moisture gain of thekth zone 206, and I_(k) is the number of infectious individuals in thekth zone 206. T₀ is the temperature of the air provided to the kth zone(e.g., as discharged by a VAV box of AHU 304), ω₀ is the humidity of theair provided to the kth zone 206, and N₀ is the infectious quantaconcentration of the air provided to the kth zone 206.

The temperature T₀ of air output by the AHU 304, the humidity ω₀ of airoutput by the AHU 304, and the infectious quanta concentration N₀ of airoutput by the AHU 304 is calculated using the equations:

$T_{0} = {{xT}_{a} + {\left( {1 - x} \right)\frac{\underset{k}{\Sigma}f_{k}T_{k}}{\underset{k}{\Sigma}f_{k}}} - {\Delta T_{c}}}$$\omega_{0} = {{x\omega_{a}} + {\left( {1 - x} \right)\frac{\underset{k}{\Sigma}f_{k}\omega_{k}}{\underset{k}{\Sigma}f_{k}}} - {\Delta\omega_{c}}}$$N_{0} = {\left( {1 - \lambda} \right)\left( {1 - x} \right)\frac{\underset{k}{\Sigma}f_{k}N_{k}}{\underset{k}{\Sigma}f_{k}}}$

where x is the fresh-air intake fraction of AHU 304, T_(a) is currentambient temperature, ω_(a) is current ambient humidity, ΔT_(c) istemperature reductions from the cooling coil of AHU 304, Δω_(c) ishumidity reduction from the cooling coil of AHU 304, and λ is afractional reduction of infectious quanta due to filtration (e.g.,operation of filter 308) and/or UV treatment (e.g., operation of UVlights 306) at AHU 304 (but not due to ventilation which is accountedfor in the factor 1−x, according to some embodiments.

In some embodiments, the dynamic models of the individual zones arestored by and used by model manager 416. Model manager 416 can store theindividual dynamic models shown above and/or aggregated models(described in greater detail below) and populate the models. Thepopulated models can then be provided by model manager 416 tooptimization manager 412 for use in performing an optimization.

In some embodiments, model manager 416 is configured to receive sensordata from sensor manager 414. Sensor manager 414 may receive sensor datafrom zone sensors 312 and/or ambient sensors 313 and provide appropriateor required sensor data to the various managers, modules, generators,components, etc., of memory 406. For example, sensor manager 414 canobtain values of the current ambient temperature T_(a), the currentambient humidity ω_(a), the temperature reduction ΔT_(c) resulting fromthe cooling coil of AHU 304, and/or the humidity reduction Δω_(c)resulting from the cooling coil of AHU 304, and provide these values tomodel manager 416 for use in determining T₀, ω₀, and N₀ or forpopulating the dynamic models of the individual zones 206.

In some embodiments, various parameters or values of the variables ofthe dynamic models of the individual zones 206 are predefined,predetermined, or stored values, or may be determined (e.g., using afunction, an equation, a table, a look-up table, a graph, a chart, etc.)based on sensor data (e.g., current environmental conditions of theambient or outdoor area, environmental conditions of the zones 206,etc.). For example, the mass density of air p may be a predeterminedvalue or may be determined based on sensor data. In some embodiments,model manager 416 can use stored values, sensor data, etc., to fullypopulate the dynamic models of the individual zones 206 (except forcontrol or adjustable variables of the dynamic models of the individualzones 206 that are determined by performing the optimization). Once themodels are populated so that only the control variables remain undefinedor undetermined, model manager 416 can provide the populated models tooptimization manager 412.

The number of infectious individuals I_(k) can be populated based onsensor data (e.g., based on biometric data of occupants or individualsof the building zones 206), or can be estimated based on sensor data. Insome embodiments, model manager 416 can use an expected number ofoccupants and various database regarding a number of infectedindividuals in an area. For example, model manager 416 can query anonline database regarding potential infection spread in the area (e.g.,number of positive tests of a particular virus or contagious illness)and estimate if it is likely that an infectious individual is in thebuilding zone 206.

In some embodiments, it can be difficult to obtain zone-by-zone valuesof the number of infectious individuals I_(k) in the modeled space(e.g., the zones 206). In some embodiments, model manager 416 isconfigured to use an overall approximation of the model for N_(k). Modelmanager 416 can store and use volume-averaged variables:

${{\overset{¯}{N} = \frac{\underset{k}{\Sigma}V_{k}N_{k}}{\overset{¯}{V}}}{\overset{¯}{f} = {\sum\limits_{k}f_{k}}}{\overset{¯}{V} = {\sum\limits_{k}V_{k}}}\overset{¯}{I}} = {\sum\limits_{k}I_{k}}$

according to some embodiments. Specifically, the equations shown aboveaggregate the variables N, f, V, and Ī across multiple zones 206 bycalculating a weighted average based on the volume of zones 206.

The K separate ordinary differential equation models (i.e., the dynamicmodels of the individual zones 206) can be added for N_(k) to determinean aggregate quantum concentration model:

${\overset{¯}{V}\frac{d\overset{¯}{N}}{dt}} = {{\sum\limits_{k}{V_{k}\frac{{dN}_{k}}{dt}}} = {{\sum\limits_{k}\left( {{f_{k}\left( {N_{0} - N_{k}} \right)} + {I_{k}q}} \right)} = {{{\overset{¯}{I}q} + {\sum\limits_{k}{f_{k}\left( {{\left( {1 - \lambda} \right)\left( {1 - x} \right)\frac{\sum\limits_{k^{\prime}}{f_{k^{\prime}}N_{k^{\prime}}}}{\sum\limits_{k^{\prime}}f_{k^{\prime}}}} - N_{k}} \right)}}} = {{{\overset{¯}{I}q} + {\left( {1 - \lambda} \right)\left( {1 - x} \right){\sum\limits_{k^{\prime}}{f_{k^{\prime}}\ N_{k^{\prime}}}}}\  - {\sum\limits_{k}{f_{k}N_{k}}}} = {{{\overset{¯}{I}q} - {\left( {\lambda + x - {\lambda x}} \right){\sum\limits_{k}{f_{k}N_{k}}}}} \approx {{\overset{¯}{I}q} - {\left( {\lambda + x - {\lambda x}} \right)\overset{\_}{f}\overset{\_}{N}}}}}}}}$

according to some embodiments, assuming that N_(k)≈N for each zone 206.The aggregate quantum concentration model is shown below:

${\overset{¯}{V}\frac{d\overset{¯}{N}}{dt}} = {{{\overset{¯}{I}q} - {\left( {\lambda + x - {\lambda x}} \right){\sum\limits_{k}{f_{k}N_{k}}}}} \approx {{\overset{¯}{I}q} - {\left( {\lambda + x - {\lambda x}} \right)\overset{¯}{f}\overset{\_}{N}}}}$

according to some embodiments.

Defining aggregate temperature, humidity, heat load, and moisture gainparameters:

${\overset{¯}{T} = \frac{\Sigma_{k}V_{k}T_{k}}{\overset{¯}{V}}}{\overset{¯}{\omega} = \frac{\underset{k}{\Sigma}V_{k}\omega_{k}}{\overset{¯}{V}}}$${\overset{¯}{Q}( \cdot )} = {\sum\limits_{k}{Q_{k}( \cdot )}}$$\overset{¯}{w} = {\sum\limits_{k}w_{k}}$

allows the k thermal models

$\rho\;{{cV}_{k}\left( \frac{{dT}_{k}}{dt} \right)}$

to be added:

${{\rho\; c\overset{¯}{V}\frac{d\overset{¯}{T}}{dt}} = {{\sum\limits_{k}{\rho\;{cV}_{k}\frac{{dT}_{k}}{dt}}} = {{\sum\limits_{k}\left( {{\rho\;{{cf}_{k}\left( {T_{0} - T_{k}} \right)}} + {Q_{k}\left( T_{k} \right)}} \right)} = {{\sum\limits_{k}{Q_{k}\left( T_{k} \right)}} + {\sum\limits_{k}{\rho\;{{cf}_{k}\left( {{xT}_{a} + {\left( {1 - x} \right)\frac{\sum\limits_{k^{\prime}}{f_{k^{\prime}}T_{k^{\prime}}}}{\sum\limits_{k^{\prime}}f_{k^{\prime}}}} - T_{k} - {\Delta T_{c}}} \right)}{\sum\limits_{k}{Q_{k}\left( T_{k} \right)}}}} + {\left( {1 - x} \right){\sum\limits_{k^{\prime}}{\rho\;{cf}_{k}}}}}}}},T_{k},{{+ {\sum\limits_{k}{\rho\;{f_{k}\left( {{xT}_{a} - T_{k} - {\Delta T_{c}}} \right)}}}} = {{{\sum\limits_{k}{Q_{k}\left( T_{k} \right)}} + {{\rho c}{\sum\limits_{k}{f_{k}\left( {{x\left( {T_{a} - T_{k}} \right)} - {\Delta T_{c}}} \right)}}}} \approx {{\overset{¯}{Q}\left( \overset{¯}{T} \right)} + {\rho\; c{\overset{¯}{f}\left( {{x\left( {T_{a} - \overset{¯}{T}} \right)} - {\Delta T_{c}}} \right)}}}}}$

according to some embodiments (assuming that T_(k)≈T for each zone 206).This yields the aggregate thermal model:

${\rho c\overset{¯}{V}\frac{d\overset{¯}{T}}{dt}} = {{{\sum\limits_{k}{Q_{k}\left( T_{k} \right)}} + {\rho c{\sum\limits_{k}{f_{k}\left( {{x\left( {T_{a} - T_{k}} \right)} - {\Delta T_{c}}} \right)}}}} \approx {{\overset{¯}{Q}\left( \overset{¯}{T} \right)} + {\rho c{\overset{¯}{f}\left( {{x\left( {T_{a} - \overset{¯}{T}} \right)} - {\Delta T_{c}}} \right)}}}}$

according to some embodiments.

The moisture model

$\rho{V_{k}\left( \frac{d\omega_{k}}{dt} \right)}$

can similarly be aggregated to yield an aggregate moisture model:

${\rho\overset{¯}{V}\frac{d\overset{¯}{\omega}}{dt}} = {{\overset{¯}{w} + {\rho{\sum\limits_{k}{f_{k}\left( {{x\left( {\omega_{a} - \omega_{k}} \right)} - {\Delta\omega_{c}}} \right)}}}} \approx {\overset{¯}{w} + {\rho{\overset{¯}{f}\left( {{x\left( {\omega_{a} - \overset{¯}{\omega}} \right)} - {\Delta\omega_{c}}} \right)}}}}$

to predict an evolution of volume-averaged humidity, according to someembodiments.

In some embodiments, model manager 416 stores and uses the aggregatequantum concentration model, the aggregate thermal model, and/or theaggregate moisture model described hereinabove. Model manager 416 canpopulate the various parameters of the aggregate models and provide theaggregate models to optimization manager 412 for use in theoptimization.

Referring still to FIG. 4, memory 406 includes optimization manager 412.

Optimization manager 412 can be configured to use the models provided bymodel manager 416 and various constraints provided by constraintgenerator 410 to construct an optimization problem for HVAC system 200(e.g., to determine design outputs and/or to determine controlparameters, setpoints, control decisions, etc., for UV lights 306 and/orAHU 304). Optimization manager 412 can construct an optimization problemthat uses the individual or aggregated temperature, humidity, and/orquantum concentration models subject to constraints to minimize energyuse. In some embodiments, decision variables of the optimization problemformulated and solved by optimization manager 412 are the flows f_(k)(or the aggregate f if the optimization problem uses the aggregatemodels), the outdoor air fraction x and the infectious quanta removalfraction λ.

The infectious quanta removal fraction A is defined as:

λ=λ_(filter)+λ_(UV)

where λ_(filter) is an infectious quanta removal fraction that resultsfrom using filter 308 (e.g., an amount or fraction of infectious quantathat is removed by filter 308), and λ_(UV) is an infectious quantaremoval fraction that results from using UV lights 306 (e.g., an amountor fraction of infectious quanta that is removed by operation of UVlights 306). In some embodiments, λ_(filter) is a design-time constant(e.g., determined based on the chosen filter 308), whereas λ_(UV) is anadjustable or controllable variable that can be determined byoptimization manager 412 by performing the optimization of theoptimization problem. In some embodiments, λ_(UV) is a discretevariable. In some embodiments, λ_(UV) is a continuous variable.

Instantaneous electricity or energy consumption of HVAC system 200 ismodeled using the equation (e.g., an objective function that isminimized):

E=η _(coil) ρf (cΔT _(c) +LΔω _(c))+η_(fan) fΔP+η _(UV)λ_(UV)

where L is a latent heat of water, ΔP is a duct pressure drop, η_(coil)is an efficiency of the cooling coil of AHU 304, η_(fan) is anefficiency of a fan of AHU 304, and η_(UV) is an efficiency of the UVlights 306, according to some embodiments. In some embodiments,optimization manager 412 is configured to store and use the energyconsumption model shown above for formulating and performing theoptimization. In some embodiments, the term η_(coil)ρf(cΔT_(c)+LΔω_(c))is an amount of energy consumed by the cooling coil or heating coil ofthe AHU 304 (e.g., over an optimization time period or time horizon),the term η_(fan) fΔP is an amount of energy consumed by the fan of theAHU 304, and η_(UV)λ_(UV) is the amount of energy consumed by the UVlights 306. In some embodiments, the duct pressure drop ΔP is affectedby or related to a choice of a type of filter 308, where higherefficiency filters 308 (e.g., filters 308 that have a higher value off_(filter)) generally resulting in a higher value of the duct pressuredrop ΔP and therefore greater energy consumption. In some embodiments, amore complex model of the energy consumption is used by optimizationmanager 412 to formulate the optimization problem (e.g., a non-linearfan model and a time-varying or temperature-dependent coil efficiencymodel).

In some embodiments, the variables ΔT_(c) and Δω_(c) for the coolingcoil of the AHU 304 are implicit dependent decision variables. In someembodiments, a value of a supply temperature T_(AHU) is selected for theAHU 304 and is used to determine the variables ΔT_(c) and Δω, based oninlet conditions to the AHU 304 (e.g., based on sensor data obtained bysensor manager 414). In such an implementation, model manager 416 oroptimization manager 412 may determine that T₀=T_(AHU) and an equationfor ω₀.

Optimization manager 412 can use the models (e.g., the individualmodels, or the aggregated models) provided by model manager 416, andconstraints provided by constraint generator 410 to construct theoptimization problem. Optimization manager 412 may formulate anoptimization problem to minimize energy consumption subject toconstraints on the modeled parameters, ω, and N and additionalconstraints:

$\begin{matrix}\min\limits_{f_{t},x_{t},\lambda_{t}} & {\sum\limits_{t}E_{t}} & \left( {{Energy}\mspace{14mu}{Cost}} \right) \\{s.t.} & \ldots & \left( {{{Dynamic}\mspace{14mu}{Models}\mspace{14mu}{for}\mspace{14mu} T_{t}},\omega_{t},{{and}\mspace{14mu} N_{t}}} \right) \\\; & \ldots & \left( {{Infection}\mspace{14mu}{Probability}\mspace{14mu}{Constraint}} \right) \\\; & {T_{t}^{\min} \leq T_{t} \leq T_{t}^{\max}} & \left( {{Temperature}\mspace{14mu}{Bounds}} \right) \\\; & {\omega_{t}^{\min} \leq \omega_{t} \leq \omega_{t}^{\max}} & \left( {{Humidity}\mspace{14mu}{Bounds}} \right) \\\; & {{x_{t}f_{t}} \geq F_{t}^{\min}} & \left( {{Fresh}\text{-}{Air}\mspace{14mu}{Ventilation}\mspace{14mu}{Bound}} \right) \\\; & {f_{t}^{\min} \leq f_{t} \leq f_{t}^{\max}} & \left( {{VAV}\mspace{14mu}{Flow}\mspace{14mu}{Bounds}} \right) \\\; & {0 \leq x_{t} \leq 1} & \left( {{Outdoor}\text{-}{Air}\mspace{14mu}{Damper}\mspace{14mu}{Bounds}} \right)\end{matrix}$

where Σ_(t) Σ_(t) is the summation of instantaneous electricity orenergy consumption of the HVAC system 200 over an optimization timeperiod, subject to the dynamic models for T_(t), ω_(t), and N_(t)(either zone-by-zone individual models, or aggregated models asdescribed above), an infection probability constraint (described ingreater detail below), temperature boundary constraints (T_(t)^(min)≤T_(t)≤T_(t) ^(max), maintaining T_(t) between a minimumtemperature boundary T_(t) ^(max) and a maximum temperature boundaryT_(t) ^(max)), humidity boundary constraints (ω_(t) ^(min)≤ω_(t)≤ω_(t)^(max), maintaining the humidity ω_(t) between a minimum humidityboundary ω_(t) ^(min) and a maximum humidity boundary x_(t)f_(t) a freshair ventilation boundary (x_(t)f_(t)≥F_(t) ^(min), maintaining the freshair ventilation x_(t)f_(t) above or equal to a minimum required amountF_(t) ^(min)), a VAV flow boundary (f_(t) ^(min)≤f_(t)≤f_(t) ^(max),maintaining the volumetric flow rate f_(t) between a minimum boundaryf_(t) ^(min) and a maximum boundary f_(t) ^(max)), and an outdoor airdamper bound/constraint (0≤x_(t)≤1 maintaining the outdoor air fractionx_(t) between 0 and 1). In some embodiments, optimization manager 412 isconfigured to discretize the dynamic models (e.g., the individualdynamic models or the aggregate dynamic models) using matrixexponentials or approximately using collocation methods.

The boundaries on temperature (T_(t) ^(min)≤T_(t)≤T_(t) ^(max)) andhumidity (ω_(t) ^(min)≤ω_(t)≤ω_(t) ^(max)) can be determined byoptimization manager 412 based on user inputs or derived from comfortrequirements. The temperature and humidity bounds may be enforced byoptimization manager 412 as soft constraints. The remaining bounds(e.g., the fresh-air ventilation bound, the VAV flow bounds, and theoutdoor-air damper bounds) can be applied to input quantities (e.g.,decision variables) by optimization manager 412 as hard constraints forthe optimization. In some embodiments, the fresh-air ventilation boundis enforced by optimization manager 412 to meet the American Society ofHeating, Refrigerating, and Air-Conditioning Engineers (ASHRAE)standards. In some embodiments, the fresh-air ventilation bound isreplaced with a model and corresponding bounds for CO2 concentration.

In some embodiments, the various constraints generated by constraintgenerator 410 or other constraints imposed on the optimization problemcan be implemented as soft constraints, hard constraints, or acombination thereof. Hard constraints may impose rigid boundaries (e.g.,maximum value, minimum value) on one or more variables in theoptimization problem such that any feasible solution to the optimizationproblem must maintain the hard constrained variables within the limitsdefined by the hard constraints. Conversely, soft constraints may beimplemented as penalties that contribute to the value of the objectivefunction (e.g., adding to the objective function if the optimizationproblem seeks to minimize the objective function or subtracting from theobjective function if the optimization problem seeks to maximize theobjective function). Soft constraints may be violated when solving theoptimization problem, but doing so will incur a penalty that affects thevalue of the objective function. Accordingly, soft constraints mayencourage optimization manager 412 to maintain the values of the softconstrained variables within the limits defined by the soft constraintswhenever possible to avoid the penalties, but may allow optimizationmanager 412 to violate the soft constraints when necessary or when doingso would result in a more optimal solution.

In some embodiments, constraint generator 410 may impose softconstraints on the optimization problem by defining large penaltycoefficients (relative to the scale of the other terms in the objectivefunction) so that optimization manager 412 only violates the softconstraints when absolutely necessary. However, it is contemplated thatthe values of the penalty coefficients can be adjusted or tuned (e.g.,by a person or automatically by constraint generator 410) to provide anoptimal tradeoff between maintaining the soft constrained variableswithin limits and the resulting cost (e.g., energy cost, monetary cost)defined by the objective function. One approach which can be used byconstraint generator 410 is to use penalties proportional to amount bywhich the soft constraint is violated (i.e., static penaltycoefficients). For example, a penalty coefficient of 0.1 $/° C.·hr for asoft constrained temperature variable would add a cost of $0.10 to theobjective function for every 1° C. that the temperature variable isoutside the soft constraint limit for every hour of the optimizationperiod. Another approach which can be used by constraint generator 410is to use variable or progressive penalty coefficients that depend onthe amount by which the soft constraint is violated. For example, avariable or progressive penalty coefficient could define a penalty costof 0.1 $/° C.·hr for the first 1° C. by which a soft constrainedtemperature variable is outside the defined limit, but a relativelyhigher penalty cost of 1.0 $/° C.·hr for any violations of the softconstrained temperature limit outside the first 1° C.

Another approach which can be used by constraint generator 410 is toprovide a “constraint violation budget” for one or more of theconstrained variables. The constraint violation budget may define atotal (e.g., cumulative) amount by which a constrained variable isallowed to violate a defined constraint limit within a given timeperiod. For example a constraint violation budget for a constrainedtemperature variable may define 30° C.·hr (or any other value) as thecumulative amount by which the constrained temperature variable isallowed to violate the temperature limit within a given time period(e.g., a day, a week, a month, etc.). This would allow the temperatureto violate the temperature constraint by 30° C. for a single hour, 1° C.for each of 30 separate hours, 0.1° C. for each of 300 separate hours,10° C. for one hour and 1° C. for each of 20 separate hours, or anyother distribution of the 30° C.·hr amount across the hours of the giventime period, provided that the cumulative temperature constraintviolation sums to 30° C.·hr or less. As long as the cumulativeconstraint violation amount is within (e.g., less than or equal to) theconstraint violation budget, constraint generator 410 may not add apenalty to the objective function or subtract a penalty from theobjective function. However, any further violations of the constraintthat exceed the constraint violation budget may trigger a penalty. Thepenalty can be defined using static penalty coefficients orvariable/progressive penalty coefficients as discussed above.

The infection probability constraint (described in greater detail below)is linear, according to some embodiments. In some embodiments, twosources of nonlinearity in the optimization problem are the dynamicmodels and a calculation of the coil humidity reduction Δω_(c). In someembodiments, the optimization problem can be solved using nonlinearprogramming techniques provided sufficient bounds are applied to theinput variables.

Infection Probability Constraint

Referring still to FIG. 4, memory 406 is shown to include a constraintgenerator 410. Constraint generator 410 can be configured to generatethe infection probability constraint, and provide the infectionprobability constraint to optimization manager 412. In some embodiments,constraint generator 410 is configured to also generate the temperaturebounds, the humidity bounds, the fresh-air ventilation bound, the VAVflow bounds, and the outdoor-air damper bounds and provide these boundsto optimization manager 412 for performing the optimization.

For the infection probability constraint, the dynamic extension of theWells-Riley equation implies that there should be an average constraintover a time interval during which an individual is in the building. Anindividual i's probability of infection P_(i,[0,T]) over a time interval[0, T] is given by:

${P_{i,{\lbrack{0,T}\rbrack}} = {1 - {\exp\left( {{- p}\;\Delta{\sum\limits_{t}{\delta_{it}N_{t}}}} \right)}}},{\delta_{it} = \left\{ \begin{matrix}1 & {{if}\mspace{14mu} i\mspace{14mu}{present}\mspace{14mu}{at}\mspace{14mu}{time}\mspace{14mu} t} \\0 & {else}\end{matrix} \right.}$

according to some embodiments. Assuming that the individual'sprobability of infection P_(i,[0,T]) is a known value, an upper boundP^(max) can be chosen for P_(i,[0,T]) and can be implemented as a linearconstraint:

${\sum\limits_{t}{\delta_{it}N_{t}}} \leq {{- \frac{1}{p\;\Delta}}{\log\left( {1 - P^{\max}} \right)}}$

according to some embodiments. In some embodiments, the variable δ_(it)may be different for each individual in the building 10 but can beapproximated as described herein.

The above linear constraint is an average constraint that givesoptimization manager 412 (e.g., an optimizer) a maximum amount offlexibility since the average constraint may allow a higherconcentration of infectious quanta during certain times of the day(e.g., when extra fresh-air ventilation is expensive due to outdoorambient conditions) as long as the higher concentrations are balanced bylower concentrations of the infectious quanta during other times of theday. However, the δ_(it) sequence may be different for each individualin the building 10. For purposes of the example described herein it isassumed that generally each individual is present a total of 8 hours(e.g., if the building 10 is an office building). However, the estimatedamount of time the individual is within the building can be adjusted orset to other values for other types of buildings. For example, when thesystems and methods described herein are implemented in a restaurant orstore, the amount of time the individual is assumed to be present in thebuilding can be set to an average or estimated amount of time requiredto complete the corresponding activities (e.g., eating a meal, shopping,etc.). While an occupancy time of the building by each individual may bereasonably known, the times that the individual is present in thebuilding may vary (e.g., the individual may be present from 7 AM to 3PM, 9 AM to 5 PM, etc.). Therefore, to ensure that the constraint issatisfied for all possible δ_(it) sequences, the constraint may berequired to be satisfied when summing over 8 hours of the day that havea highest concentration.

This constraint is represented using linear constraints as:

${{{{M\eta} + {\sum\limits_{t}\mu_{t}}} \leq {{- \frac{1}{p\;\Delta}}{\log\left( {1 - P^{\max}} \right)}}}{\mu_{t} + \eta}} \geq {N_{t}\ \text{∀}t}$

where η and μ_(t) are new auxiliary variables in the optimizationproblem, and M is a number of discrete timesteps corresponding to 8hours (or any other amount of time that an individual is expected tooccupy building 10 or one of building zones 206). This formulation maywork since η is set to an Mth highest value of N_(t) and each of theμ_(t) satisfy μ_(t)=max(N_(t)−η, 0). Advantageously, this implementationof the infection probability constraint can be generated by constraintgenerator 410 and provided to optimization manager 412 for use in theoptimization problem when controller 310 is implemented to performcontrol decisions for HVAC system 200 (e.g., when controller 310operates in an on-line mode).

An alternative implementation of the infection probability constraint isshown below that uses a pointwise constraint:

${N_{t} \leq N_{t}^{\max}} = {{- \frac{1}{{Mp}\;\Delta}}{\log\left( {1 - P^{\max}} \right)}}$

where N_(t) is constrained to be less than or equal to N_(t) ^(NIX) fora maximum infection probability value P^(max). In some embodiments, thepointwise constraint shown above is generated by constraint generator410 for when optimization manager 412 is used in an off-line or designimplementation. In some embodiments, the pointwise constraint shownabove, if satisfied in all zones 206, ensures that any individual willmeet the infection probability constraint. Such a constraint maysacrifice flexibility compared to the other implementation of theinfection probability constraint described herein, but translates to asimple box constraint similar to the other bounds in the optimizationproblem, thereby facilitating a simpler optimization process.

In some embodiments, the maximum allowable or desirable infectionprobability P^(max) is a predetermined value that is used by constraintgenerator 410 to generate the infection probability constraintsdescribed herein. In some embodiments, constraint generator 410 isconfigured to receive the maximum allowable or desirable infectionprobability P^(max) from a user as a user input. In some embodiments,the maximum allowable or desirable infection probability P^(max) is anadjustable parameter that can be set by a user or automaticallygenerated based on the type of infection, time of year, type or use ofthe building, or any of a variety of other factors. For example, somebuildings (e.g., hospitals) may be more sensitive to preventing diseasespread than other types of buildings and may use lower values ofP^(max). Similarly, some types of diseases may be more serious orlife-threatening than others and therefore the value of P^(max) can beset to relatively lower values as the severity of the disease increases.In some embodiments, the value of P^(max) can be adjusted by a user andthe systems and methods described herein can run a plurality ofsimulations or optimizations for a variety of different values ofP^(max) to determine the impact on cost and disease spread. A user canselect the desired value of P^(max) in view of the estimated cost andimpact on disease spread using the results of the simulations oroptimizations.

Model Enhancements

Referring still to FIG. 4, optimization manager 412, constraintgenerator 410, and/or model manager 416 can implement various modelenhancements in the optimization. In some embodiments, optimizationmanager 412 is configured to add a decision variable for auxiliary(e.g., controlled) heating (e.g., via baseboard heat or VAV reheatcoils). In some embodiments, an effect of the auxiliary heating isincluded in the dynamic model of temperature similar to the disturbanceheat load Q_(k)(⋅). Similar to the other decision variables, theauxiliary heating decision variable may be subject to bounds (e.g., withboth set to zero during cooling season to disable auxiliary heating)that are generated by constraint generator 410 and used by optimizationmanager 412 in the optimization problem formulation and solving. In someembodiments, the auxiliary heating also results in optimization manager412 including another term for associated energy consumption in theenergy consumption equation (shown above) that is minimized.

In some embodiments, certain regions or areas may have variableelectricity prices and/or peak demand charges. In some embodiments, theobjective function (e.g., the energy consumption equation) can beaugmented by optimization manager 412 to account for such coststructures. For example, the existing energy consumption Σ_(t) that isminimized by optimization manager 412 may be multiplied by acorresponding electricity price P_(t). A peak demand charge may requirethe use of an additional parameter e_(t) that represents a base electricload of building 10 (e.g., for non-HVAC purposes). Optimization manager412 can include such cost structures and may minimize overall costassociated with electricity consumption rather than merely minimizingelectrical consumption. In some embodiments, optimization manager 412accounts for revenue which can be generated by participating inincentive based demand response (IBDR) programs, frequency regulation(FR) programs, economic load demand response (ELDR) programs, or othersources of revenue when generating the objective function. In someembodiments, optimization manager 412 accounts for the time value ofmoney by discounting future costs or future gains to their net presentvalue. These and other factors which can be considered by optimizationmanager 412 are described in detail in U.S. Pat. No. 10,359,748 grantedJul. 23, 2019, U.S. Patent Application Publication No. 2019/0347622published Nov. 14, 2019, and U.S. Patent Application Publication No.2018/0357577 published Dec. 13, 2018, each of which is incorporated byreference herein in its entirety.

In some embodiments, certain locations have time-varying electricitypricing, and therefore there exists a potential to significantly reducecooling costs by using a solid mass of building 10 for thermal energystorage. In some embodiments, controller 310 can operate to pre-cool thesolid mass of building 10 when electricity is cheap so that the solidmass can later provide passive cooling later in the day when electricityis less expensive. In some embodiments, optimization manager 412 and/ormodel manager 416 are configured to model this effect using a modelaugmentation by adding a new variable T_(r) ^(m) to represent the solidmass of the zone 206 evolving as:

${\rho c_{m}V_{k}^{m}\frac{{dT}_{k}^{m}}{dt}} = {h_{k}^{m}\left( {T_{k} - T_{k}^{m}} \right)}$

with a corresponding term:

${\rho cV_{k}\frac{dT_{k}}{dt}} = {\ldots + {h_{k}^{m}\left( {T_{k}^{m} - T_{k}} \right)}}$

added to the air temperature model (shown above). This quantity can alsobe aggregated by model manager 416 to an average value T ^(m) similar toT.

For some diseases, infectious particles may naturally become deactivatedor otherwise removed from the air over time. To consider these effects,controller 310 can add a proportional decay term to the infectiousquanta model (in addition to the other terms of the infectious quantamodel discussed above). An example is shown in the following equation:

${V\frac{dN}{dt}} = {\ldots - {V\;\beta\; N}}$

where β represents the natural decay rate (in s⁻¹) of the infectiousspecies and the ellipsis represents the other terms of the infectiousquanta model as discussed above. Because the natural decay subtractsfrom the total amount of infectious particles, the natural decay term issubtracted from the other terms in the infectious quanta model. Forexample, if a given infectious agent has a half-life t_(1/2) of one hour(i.e., t_(1/2)=1 hr=3600 s), then the corresponding decay rate is givenby:

$\beta = {\frac{\ln(2)}{t_{1/2}} \approx {{1.9}25 \times 10^{- 4}s^{- 1}}}$

This extra term can ensure that infectious particle concentrations donot accumulate indefinitely over extremely long periods of time.

Off-Line Optimization

Referring particularly to FIG. 5, controller 310 can be configured foruse as a design or planning tool for determining various designparameters of HVAC system 300 (e.g., for determining a size of filter308, UV lights 306, etc.). In some embodiments, controller 310implemented as a design tool, a planning tool, a recommendation tool,etc., (e.g., in an off-line mode) functions similarly to controller 310implemented as a real-time control device (e.g., in an on-line mode).However, model manager 416, constraint generator 410, and optimizationmanager 412 may receive required sensor input data (i.e., modelpopulation data) from a simulation database 424. Simulation database 424can store values of the various parameters of the constraints orboundaries, the dynamic models, or typical energy consumption costs oroperational parameters for energy-consuming devices of the HVAC system200. In some embodiments, simulation database 424 also stores predictedor historical values as obtained from sensors of HVAC system 200. Forexample, simulation database 424 can store typical ambient temperature,humidity, etc., conditions for use in performing the off-linesimulation.

When controller 310 is configured for use as the design tool (shown inFIG. 5), controller 310 may receive user inputs from user input device420. The user inputs may be initial inputs for various constraints(e.g., a maximum value of the probability of infection for thesimulation) or various required input parameters. The user can alsoprovide simulation data for simulation database 424 used to populate themodels or constraints, etc. Controller 310 can output suggestions ofwhether to use a particular piece of equipment (e.g., whether or not touse or install UV lights 306), whether to use AHU 304 to draw outsideair, etc., or other factors to minimize cost (e.g., to optimize theobjective function, minimize energy consumption, minimize energyconsumption monetary cost, etc.) and to meet disinfection goals (e.g.,to provide a desired level of infection probability). In someembodiments, controller 310 may provide different recommendations orsuggestions based on a location of building 10. In some embodiments, therecommendations notify the user regarding what equipment is needed tokeep the infection probability of zones 206 within the threshold whilenot increasing energy cost or carbon footprint.

Compared to the on-line optimization (described in greater detailbelow), the optimization problem formulated by optimization manager 412for the off-line implementation includes an additional constraint on theinfectious quanta concentration (as described in greater detail above).In some embodiments, the infectious quanta concentration can becontrolled or adjusted by (a) changing the airflow into each zone 206(e.g., adjusting f_(i)), (b) changing the fresh-air intake fraction(e.g., adjusting x), or (c) destroying infectious particles in the AHU304 via filtration or UV light (e.g., adjusting λ).

It should be noted that the first and second control or adjustments(e.g., (a) and (b)) may also affect temperature and humidity of thezones 206 of building 10. However, the third control option (c) (e.g.,adjusting the infectious quanta concentration through filtration and/oroperation of UV lights) is independent of the temperature and humidityof the zones 206 of building 10 (e.g., does not affect the temperatureor humidity of zones 206 of building 10). In some embodiments,optimization manager 412 may determine results that rely heavily orcompletely on maintaining the infectious quanta concentration below itscorresponding threshold or bound through operation of filter 308 and/orUV lights 306. However, there may be sufficient flexibility in thetemperature and humidity of building zone 206 so that optimizationmanager 412 can determine adjustments to (a), (b), and (c)simultaneously to achieve lowest or minimal operating costs (e.g.,energy consumption). Additionally, since purchasing filters 308 and/orUV lights 306 may incur significant capital costs (e.g., to purchasesuch devices), controller 310 may perform the optimization as asimulation to determine if purchasing filters 308 and/or UV lights 306is cost effective.

When controller 310 is configured as the design tool shown in FIG. 5,controller 310 may provide an estimate of a total cost (both capitalcosts and operating costs) to achieve a desired level of infectioncontrol (e.g., to maintain the infection probability below or at adesired amount). The purpose is to run a series of independentsimulations, assuming different equipment configurations (e.g., asstored and provided by simulation database 424) and for differentinfection probability constraints given typical climate and occupancydata (e.g., as stored and provided by simulation database 424). In someembodiments, the different equipment configurations include scenarioswhen filters 308 and/or UV lights 306 are installed in the HVAC system200, or when filters 308 and/or UV lights 306 are not installed in theHVAC system 200.

After performing the simulation for different equipment configurationscenarios and/or different infection probability constraints, controller310 can perform a cost benefit analysis based on global design decisions(e.g., whether or not to install UV lights 306 and/or filters 308). Thecost benefit analysis may be performed by results manager 418 and thecost benefit analysis results can be output as display data to abuilding manager via display device 422. These results may aid thebuilding manager or a building designer in assessing potential optionsfor infection control of building 10 (as shown in FIG. 8).

Referring particularly to FIGS. 5 and 8, graph 800 illustrates apotential output of results manager 418 that can be displayed by displaydevice 422. Graph 800 illustrates relative cost (the Y-axis) withrespect to infection probability (the X-axis) for a case when bothfiltration and UV lights are used for infection control (represented byseries 808), a case when filtration is used for infection controlwithout using UV lights (represented by series 802), a case when UVlights are used for infection control without using filtration(represented by series 806), and a case when neither UV lights andfiltration are used for infection control (represented by series 804).In some embodiments, each of the cases illustrated by series 802-808assume that fresh-air intake is used to control infection probability.Data associated with graph 800 can be output by results manager 418 sothat graph 800 can be generated and displayed on display device 422.

In some embodiments, the off-line optimization performed by optimizationmanager 412 is faster or more computationally efficient than the on-lineoptimization performed by optimization manager 412. In some embodiments,the simulation is performed using conventional rule-based control ratherthan a model-predictive control scheme used for the on-lineoptimization. Additionally, the simulation may be performed over shortertime horizons than when the optimization is performed in the on-linemode to facilitate simulation of a wide variety of design conditions.

In some embodiments, optimization manager 412 is configured to use theaggregate dynamic models as generated, populated, and provided by modelmanager 416 for the off-line optimization (e.g., the designoptimization). When optimization manager 412 uses the aggregate dynamicmodels, this implies that there are three decision variables of theoptimization: f, x, and λ. The variable λ can include two positions ateach timestep (e.g., corresponding to the UV lights 306 being on or theUV lights 306 being off). A reasonable grid size of f and x may be 100.Accordingly, this leads to 100×100×2=20,000 possible combinations ofcontrol decisions at each step, which is computationally manageable.Therefore, optimization manager 412 can select values of the variablesf, x, and λ via a one-step restriction of the optimization problem bysimply evaluating all possible sets of control inputs and selecting theset of control inputs that achieves a lowest cost.

If additional variables are used, such as an auxiliary heating variable,this may increase the dimensionality of the optimization problem.However, optimization manager 412 can select a coarser grid (e.g., 5 to10 choices) for the additional variable.

In some embodiments, optimization manager 412 is configured to solve anumber of one-step optimization problems (e.g., formulate differentoptimization problems for different sets of the control variables andsolve the optimization problem over a single timestep) in a trainingperiod, and then train a function approximator (e.g., a neural network)to recreate a mapping. This can improve an efficiency of theoptimization. In some embodiments, optimization manager 412 isconfigured to apply a direct policy optimization to the dynamic modelsin order to directly learn a control law using multiple paralleloptimization problems.

In some embodiments, when controller 310 functions as the design toolshown in FIG. 5, there are two design variables. The first designvariable is whether it is cost effective or desirable to purchase andinstall UV lights 306, and the second design variable is whether it iscost effective or desirable to purchase and install filters 308 (e.g.,advanced filtration devices).

In some embodiments, optimization manager 412 is configured to perform avariety of simulations subject to different simulation variables foreach simulation month. These simulation variables can be separated intoa design decision category and a random parameter category. The designdecision category includes variables whose values are chosen by systemdesigners, according to some embodiments. The random parameters categoryincludes variables whose values are generated by external (e.g., random)processes.

The design decision category can include a first variable of whether toactivate UV lights 306. The first variable may have two values (e.g., afirst value for when UV lights 306 are activated and a second value forwhen UV lights 306 are deactivated). The design decision category caninclude a second decision variable of which of a variety ofhigh-efficiency filters to use, if any. The second variable may have anynumber of values that the building manager wishes to simulate (e.g., 5)and can be provided via user input device 420. The design decisionscategory can also include a third variable of what value should be usedfor the infection probability constraint (as provided by constraintgenerator 410 and used in the optimization problem by optimizationmanager 412). In some embodiments, various values of the third variableare also provided by the user input device 420. In some embodiments,various values of the third variable are predetermined or stored insimulation database 424 and provided to optimization manager 412 for usein the simulation. The third variable may have any number of values asdesired by the user (e.g., 3 values).

The random parameters category can include an ambient weather and zoneoccupancy variable and a number of infected individuals that are presentin building 10 variable. In some embodiments, the ambient weather andzone occupancy variable can have approximately 10 different values. Insome embodiments, the number of infected individuals present can haveapproximately 5 different values.

In order to determine a lowest cost for a given month, optimizationmanager 412 can aggregate the variables in the random parameterscategory (e.g., average) and then perform an optimization to minimizethe energy consumption or cost over feasible values of the variables ofthe design decisions category. In some embodiments, some of thedesign-decision scenarios are restricted by a choice of global designdecisions. For example, for optimization manager 412 to calculatemonthly operating costs assuming UV lights 306 are chosen to beinstalled but not filtration, optimization manager 412 may determinethat a lowest cost scenario across all scenarios is with no filtrationbut with the UV lights 306 enabled or disabled. While this may beunusual (e.g., for the UV lights 306 to be disabled) even though the UVlights 306 are installed, various conditions (e.g., such as weather) maymake this the most cost effective solution.

In some embodiments, simulation logic performed by optimization manager412 may be performed in a Tensorflow (e.g., as operated by a laptopcomputer, or any other sufficiently computationally powerful processingdevice). In order to perform 1,500 simulation scenarios for each month,or 18,000 for an entire year, with a timestep of 15 minutes, thisimplies a total of approximately 52 million timesteps of scenarios for agiven simulation year.

In some embodiments, optimization manager 412 requires varioussimulation data in order to perform the off-line simulation (e.g., todetermine the design parameters). In some embodiments, the simulationdata is stored in simulation database 424 and provided to any ofconstraint generator 410, model manager 416, and/or optimization manager412 as required to perform their respective functions. The simulationdata stored in simulation database 424 can include heat-transferparameters for each zone 206, thermal and moisture loads for each zone206, coil model parameters of the AHU 304, fan model parameters of theAHU 304, external temperature, humidity, and solar data, filtrationefficiency, pressure drop, and cost versus types of the filter 308,disinfection fraction and energy consumption of the UV lights 306,installation costs for the UV lights 306 and the filter 308, typicalbreathing rate p, a number of infected individuals Ī in building zones206, and disease quanta generation q values for various diseases. Insome embodiments, the heat-transfer parameters for each zone 206 may beobtained by simulation database 424 from previous simulations or fromuser input device 420. In some embodiments, the thermal and moistureloads for each zone 206 are estimated based on an occupancy of the zones206 and ASHRAE guidelines. After this simulation data is obtained insimulation database 424, controller 310 may perform the simulation(e.g., the off-line optimization) as described herein.

It should be understood that as used throughout this disclosure, theterm “optimization” may signify a temporal optimization (e.g., across atime horizon) or a static optimization (e.g., at a particular moment intime, an instantaneous optimization). In some embodiments, optimizationmanager 412 is configured to either run multiple optimizations fordifferent equipment selections, or is configured to treat equipmentconfigurations as decision variables and perform a single optimizationto determine optimal equipment configurations.

It should also be understood that the term “design” as used throughoutthis disclosure (e.g., “design data” and/or “design tool”) may includeequipment recommendations (e.g., recommendations to purchase particularequipment or a particular type of equipment such as a particular filter)and/or operational recommendations for HVAC system 200. In other words,“design data” as used herein may refer to any information, metrics,operational data, guidance, suggestion, etc., for selecting equipment,an operating strategy, or any other options to improve financial metricsor other control objectives (e.g., comfort and/or infectionprobability).

For example, controller 310 as described in detail herein with referenceto FIG. 5 may be configured to provide recommendations of specificmodels to purchase. In some embodiments, controller 310 is configured tocommunicate with an equipment performance database to provideproduct-specific selections. For example, controller 310 can search thedatabase for equipment that has particular specifications as determinedor selected by the optimization. In some embodiments, controller 310 mayalso provide recommended or suggested control algorithms (e.g., modelpredictive control) as the design data. In some embodiments, controller310 may provide a recommendation or suggestion of a general type ofequipment or a general equipment configuration without specifying aparticular model. In some embodiments, controller 310 may also recommenda specific filter or a specific filter rating. For example, optimizationmanager 412 can perform multiple optimizations with different filterratings and select the filter ratings associated with an optimal result.

On-Line Optimization

Referring again to FIG. 4, controller 310 can be implemented as anon-line controller that is configured to determine optimal control forthe equipment of building 10. Specifically, controller 310 may determineoptimal operation for UV lights 306 and AHU 304 to minimize energyconsumption after UV lights 306 and/or filter 308 are installed and HVACsystem 200 is operational. When controller 310 is configured as anon-line controller, controller 310 may function similarly to controller310 as configured for off-line optimization and described in greaterdetail above with reference to FIG. 5. However, controller 310 candetermine optimal control decisions for the particular equipmentconfiguration of building 10.

In some embodiments, optimization manager 412 is configured to performmodel predictive control similar to the techniques described in U.S.patent application Ser. No. 15/473,496, filed Mar. 29, 2017, the entiredisclosure of which is incorporated by reference herein.

While optimization manager 412 can construct and optimize theoptimization problem described in greater detail above, and shown below,using MPC techniques, a major difference is that optimization manager412 performs the optimization with an infectious quanta concentrationmodel as described in greater detail above.

$\begin{matrix}\min\limits_{f_{t},x_{t},\lambda_{t}} & {\sum\limits_{t}E_{t}} & \left( {{Energy}\mspace{14mu}{Cost}} \right) \\{s.t.} & \ldots & \left( {{{Dynamic}\mspace{14mu}{Models}\mspace{14mu}{for}\mspace{14mu} T_{t}},\omega_{t},{{and}\mspace{14mu} N_{t}}} \right) \\\; & \ldots & \left( {{Infection}\mspace{14mu}{Probability}\mspace{14mu}{Contraint}} \right) \\\; & {T_{t}^{\min} \leq T_{t} \leq T_{t}^{\max}} & \left( {{Tempurature}\mspace{14mu}{Bounds}} \right) \\\; & {\omega_{t}^{\min} \leq \omega_{t} \leq \omega_{t}^{\max}} & \left( {{Humidity}\mspace{14mu}{Bounds}} \right) \\\; & {{x_{t}f_{t}} \geq F_{t}^{\min}} & \left( {{Fresh}\text{-}{Air}\mspace{14mu}{Ventilation}\mspace{14mu}{Bounds}} \right) \\\; & {f_{t}^{\min} \leq f_{t} \leq f_{t}^{\max}} & \left( {{VAV}\mspace{14mu}{Flow}\mspace{14mu}{Bounds}} \right) \\\; & {0 \leq x_{t} \leq 1} & \left( {{Outdoor}\text{-}{Air}\mspace{14mu}{Damper}\mspace{14mu}{Bounds}} \right)\end{matrix}$

Therefore, the resulting optimization problem has additional constraintson this new variable (the infectious quanta concentration) but also newflexibility by determined decisions for activating UV lights 306. Insome embodiments, the optimization performed by optimization manager 412can balance, in real time, a tradeoff between takin gin additionaloutdoor air (which generally incurs a cooling energy penalty) andactivating the UV lights 306 (which requires electricity consumption).Additionally, the addition of infectious agent control can also provideadditional room optimization of HVAC system 200 during a heating season(e.g., during winter). Without considering infectious quantaconcentrations, solutions generally lead to a minimum outdoor airflowbelow a certain break-even temperature, below which heating is requiredthroughout building 10. However, since the optimization problemformulated by optimization manager 412 can determine to increase outdoorair intake, this can provide an additional benefit of disinfection.

For purposes of real-time or on-line optimization, the HVAC system 200can be modeled on a zone-by-zone basis due to zones 206 each havingseparate temperature controllers and VAV boxes. In some embodiments,zone-by-zone temperature measurements are obtained by controller 310from zone sensors 312 (e.g., a collection of temperature, humidity, CO2,air quality, etc., sensors that are positioned at each of the multiplezones 206). In some embodiments, optimization manager 412 is configuredto use zone-level temperature models but aggregate humidity andinfectious quanta models for on-line optimization. Advantageously, thiscan reduce a necessary modeling effort and a number of decisionvariables in the optimization problem. In some embodiments, if the AHU304 serves an excessive number of zones 206, the zone-level thermalmodeling may be too computationally challenging so optimization manager412 can use aggregate temperature models.

After optimization manager 412 has selected whether to use individual oraggregate models (or some combination thereof), optimization manager 412can implement a constraint in the form:

$\frac{dx}{dt} = {{{f\left( {{x(t)},{u(t)},{p(t)}} \right)}\mspace{14mu}{for}\mspace{14mu}{all}\mspace{14mu} t} \in \left\lbrack {0,T} \right\rbrack}$

given a horizon t, where u(t) is a decision, control, or adjustablevariable, and p(t) are time-varying parameters (the values of which areforecasted ahead of time). In some embodiments, optimization manager 412is configured to implement such a constraint by discretizing the u(t)and p(t) signals into piecewise-constant values u_(n) and p_(n) wherethe discrete index n represents the time interval t∈[nΔ, (n+1)Δ] for afixed sample time Δ. Optimization manager 412 may then transform theconstraint to:

$\frac{dx}{dt} = {{{f\left( {{x(t)},u_{j},p_{j}} \right)}\mspace{14mu}{for}\mspace{14mu}{all}\mspace{14mu} t} \in {\left\lbrack {{n\;\Delta},{\left( {n + 1} \right)\Delta}} \right\rbrack\mspace{14mu}{and}\mspace{14mu} n} \in \left\{ {0,\ldots\mspace{14mu},{N - 1}} \right\}}$

where N=T/Δ the total number of timesteps. In some embodiments,optimization manager 412 is configured to evaluate this constraint usingadvanced quadrature techniques. For example, optimization manager 412may transform the constraint to:

x _(n+1) =F(x _(n) ,u _(n) ,p _(n))

where x(t) is discretized to x_(n) and F(⋅) represents a numericalquadrature routine. In some embodiments, if the models provided by modelmanager 416 are sufficiently simple, optimization manager 412 can derivean analytical expression for F(⋅) to perform this calculation directly.

In some embodiments, optimization manager 412 uses an approximatemidpoint method to derive the analytical expression:

$x_{n + 1} = {x_{k} + {{f\left( {\frac{x_{n + 1} + x_{n}}{2},u_{n},p_{n}} \right)}\Delta}}$

where the ordinary differential equation f(⋅) is evaluated at a midpointof the time interval.

In some embodiments, optimization manager 412 is configured torepeatedly solve the optimization problem at regular intervals (e.g.,every hour) to revise an optimized sequence of inputs for control signalgenerator 408. However, since the optimization is nonlinear andnonconvex, it may be advantageous to decrease a frequency at which theoptimization problem is solved to provide additional time to retryfailed solutions.

In some embodiments, optimization manager 412 uses a daily advisorycapacity. For example, optimization manager 412 may construct and solvethe optimization problem once per day (e.g., in the morning) todetermine optimal damper positions (e.g., of AHU 304), UV utilizations(e.g., operation of UV lights 306), and zone-level airflows. Using theresults of this optimization, optimization manager 412 may be configuredto pre-schedule time-varying upper and lower bounds on the variousvariables of the optimized solution, but with a range above and below sothat optimization manager 412 can have sufficient flexibility to rejectlocal disturbances. In some embodiments, regulatory control systems ofHVAC system 200 are maintained but may saturate at new tighter boundsobtained from the optimization problem. However, optimization manager412 may be configured to re-optimize during a middle of the day ifambient sensor data from ambient sensors 314 (e.g., ambient temperature,outdoor temperature, outdoor humidity, etc.) and/or weather forecastsand/or occupancy forecasts indicate that the optimization should bere-performed (e.g., if the weather forecasts are incorrect or change).

In some embodiments, optimization manager 412 is configured to reduce anamount of optimization by training a neural network based on results ofmultiple offline optimal solutions (e.g., determined by controller 310when performing off-line optimizations). In some embodiments, the neuralnetwork is trained to learn a mapping between initial states anddisturbance forecasts to optimal control decisions. The neural networkcan be used in the online implementation of controller 310 as asubstitute for solving the optimization problem. One advantage of usinga neural network is that the neural network evaluation is faster thanperforming an optimization problem, and the neural network is unlikelyto suggest poor-quality local optima (provided such solutions areexcluded from the training data). The neural network may, however,return nonsensical values for disturbance sequences. However, thisdownside may be mitigated by configuring controller 310 to use a hybridtrust-region strategy in which optimization manager 412 solves theoptimization problem via direct optimization at a beginning of the day,and then for the remainder of the day, controller 310 usesneural-network suggestions if they are within a predefined trust regionof the optimal solution. If a neural-network suggestion is outside ofthe predefined trust region, optimization manager 412 may use a previousoptimal solution that is within the predefined trust region.

In some embodiments, the optimization problem is formulated byoptimization manager 412 assuming the zone-level VAV flows f_(k) are thedecision variables. In some systems, however, a main interface betweencontroller 310 and equipment of HVAC system 200 is temperature setpointsthat are sent to zone-level thermostats. In some embodiments,optimization manager 412 and control signal generator 408 are configuredto shift a predicted optimal temperature sequence backward by one timeinterval and then pass these values (e.g., results of the optimization)as the temperature setpoint. For example, if the forecasts over-estimatehead loads in a particular zone 206, then a VAV damper for that zonewill deliver less airflow to the zone 206, since less cooling isrequired to maintain a desired temperature.

When optimization manager 412 uses the constraint on infectious quantaconcentration, controller 310 can now use the zone-level airflow tocontrol two variables, while the local controllers are only aware ofone. Therefore, in a hypothetical scenario, the reduced airflow mayresult in a violation of the constraint on infection probability. Insome embodiments, optimization manager 412 and/or control signalgenerator 408 are configured to maintain a higher flow rate at the VAVeven though the resulting temperature may be lower than predicted. Toaddress this situation, optimization manager 412 may use the minimum andmaximum bounds on the zone-level VAV dampers, specifically setting themto a more narrow range so that the VAV dampers are forced to deliver (atleast approximately) an optimized level of air circulation. In someembodiments, to meet the infectious quanta concentration, the relevantbound is the lower flow limit (as any higher flow will still satisfy theconstraint, albeit at higher energy cost). In some embodiments, asuitable strategy is to set the VAV minimum position at the level thatdelivers 75% to 90% of the optimized flow. In some embodiments, a VAVcontroller is free to dip slightly below the optimized level whenoptimization manager 412 over-estimates heat loads, while also havingthe full flexibility to increase flow as necessary when optimizationmanager 412 under-estimates heat loads. In the former case, optimizationmanager 412 may slightly violate the infectious quanta constraint (whichcould potentially be mitigated via rule-based logic to activate UVlights 306 if flow drops below planned levels), while in the lattercase, the optimal solution still satisfies the constraint on infectiousquanta. Thus, optimization manager 412 can achieve both control goalswithout significant disruption to the low-level regulatory controlsalready in place.

On-Line Optimization Process

Referring particularly to FIG. 6, a process 600 for performing anon-line optimization to minimize energy consumption and satisfy aninfection probability constraint in a building is shown, according tosome embodiments. Process 600 can be performed by controller 310 whencontroller 310 is configured to perform an on-line optimization. In someembodiments, process 600 is performed in real time for HVAC system 200to determine optimal control of AHU 304 and/or UV lights 306. Process600 can be performed for an HVAC system that includes UV lights 306configured to provide disinfection for supply air that is provided toone or more zones 206 of a building 10, filter 308 that filters an airoutput of an AHU, and/or an AHU (e.g., AHU 304). Process 600 can also beperformed for HVAC systems that do not include filter 308 and/or UVlights 306.

Process 600 includes determining a temperature model for each ofmultiple zones to predict a temperature of a corresponding zone based onone or more conditions or parameters of the corresponding zone (step602), according to some embodiments. The temperature model can begenerated or determined by model manager 416 for use in an optimizationproblem. In some embodiments, the temperature model is:

${\rho\;{{cV}_{k}\left( \frac{dT_{k}}{dt} \right)}} = {{\rho c{f_{k}\left( {T_{0} - T_{k}} \right)}} + {Q_{k}\left( T_{k} \right)}}$

where ρ is a mass density of air, c is a heat capacity of air, V_(k) isa volume of the kth zone, f_(k) is a volumetric flow of air into the kthzone, T₀ is the temperature of air output by the AHU, T_(k) is thetemperature of the kth zone, and Q_(k) is the heat load on the kth zone.Step 602 can be performed by model manager 416 as described in greaterdetail above with reference to FIGS. 4-5.

Process 600 includes determining a humidity model for each of themultiple zones to predict a humidity of the corresponding zone based onone or more conditions or parameters of the corresponding zone (step604), according to some embodiments. Step 604 can be similar to step 602but for the humidity model instead of the temperature model. In someembodiments, the humidity model is:

${\rho{V_{k}\left( \frac{d\omega_{k}}{dt} \right)}} = {{\rho\;{f\left( {\omega_{0} - T_{0}} \right)}} + w_{k}}$

for a kth zone 206. In some embodiments, step 604 is performed by modelmanager 416 as described in greater detail above with reference to FIGS.4-5.

Process 600 incudes determining an infectious quanta concentration modelfor each of the multiple zones to predict an infectious quanta of thecorresponding zone based on one or more conditions or parameters of thecorresponding zone (step 606), according to some embodiments. In someembodiments, the infectious quanta concentration model is similar to thehumidity model of step 604 or the temperature model of step 602. Theinfectious quanta concentration model can be:

${V_{k}\left( \frac{{dN}_{k}}{dt} \right)} = {{f_{k}\left( {N_{0} - N_{k}} \right)} + {I_{k}q}}$

according to some embodiments. In some embodiments, step 606 isperformed by model manager 416.

Process 600 includes determining an aggregated temperature model, anaggregated humidity model, an aggregated infectious quanta model, anaggregated thermal model, and an aggregated moisture model (step 608),according to some embodiments. In some embodiments, step 608 isoptional. Step 608 can include generating or determining each of theaggregated models by determining a volume-average across zones 206. Theaggregate infectious quanta model is:

${\overset{\_}{V}\frac{d\overset{\_}{N}}{dt}} = {{{\overset{\_}{I}q} - {\left( {\lambda + x - {\lambda x}} \right){\sum\limits_{k}{f_{k}N_{k}}}}} \approx {{\overset{\_}{I}q} - {\left( {\lambda + x - {\lambda x}} \right)\overset{\_}{f}\overset{\_}{N}}}}$

according to some embodiments. The aggregated thermal model is:

${\rho\; c\overset{\_}{V}\frac{d\overset{\_}{T}}{dt}} = {{{\sum\limits_{k}{Q_{k}\left( T_{k} \right)}} + {\rho c{\sum\limits_{k}{f_{k}\left( {{x\left( {T_{a} - T_{k}} \right)} - {\Delta T_{c}}} \right)}}}} \approx {{\overset{\_}{Q}\left( \overset{\_}{T} \right)} + {\rho\; c{\overset{\_}{f}\left( {{x\left( {T_{a} - \overset{\_}{T}} \right)} - {\Delta T_{c}}} \right)}}}}$

according to some embodiments. The aggregated moisture model is:

${\rho\overset{\_}{V}\frac{d\;\overset{\_}{\omega}}{dt}} = {{\overset{\_}{w} + {\rho{\sum\limits_{k}{f_{k}\left( {{x\left( {\omega_{a} - \omega_{k}} \right)} - {\Delta\omega_{c}}} \right)}}}} \approx {\overset{\_}{w} + {\rho{\overset{\_}{f}\left( {{x\left( {\omega_{a} - \overset{\_}{\omega}} \right)} - {\Delta\omega_{c}}} \right)}}}}$

according to some embodiments. In some embodiments, the aggregatedthermal and moisture models are aggregate thermal models. Step 608 canbe optional. Step 608 can be performed by model manager 416.

Process 600 includes populating any of the temperature model, thehumidity model, the infectious quanta model, or the aggregated modelsusing sensor data or stored values (step 610), according to someembodiments. In some embodiments, step 610 is performed by model manager416. In some embodiments, step 610 is optional. Step 610 can beperformed based on sensor data obtained from zone sensors 312.

Process 600 includes determining an objective function including a costof operating an HVAC system that serves the zones (step 612), accordingto some embodiments. In some embodiments, step 612 is performed byoptimization manager 412 using the dynamic models and/or the aggregatedmodels provided by model manager 416. The objective function may be asummation of the energy consumption, energy cost, or other variable ofinterest over a given time period. The instantaneous energy consumptionat a discrete time step is given by:

E=η _(coil) ρf (cΔT _(c) +LΔω _(c))+η_(fan) fΔP+η _(UV)λ_(UV)

which can be summed or integrated over all time steps of the given timeperiod as follows:

${\int_{0}^{T}{{E(t)}dt}} \approx {\Delta{\sum\limits_{t}E_{t}}}$

where Δ is the duration of a discrete time step, according to someembodiments.

Process 600 includes determining one or more constraints for theobjective function including an infection probability constraint (step614), according to some embodiments. In some embodiments, step 614 isperformed by constraint generator 410. The one or more constraints caninclude the infection probability constraint, temperature bounds orconstraints, humidity bounds or constraints, fresh-air ventilationbounds or constraints, VAV flow bounds or constraints, and/oroutdoor-air damper bounds or constraints. The infection probabilityconstraint is:

${{{{M\eta} + {\sum\limits_{t}\mu_{t}}} \leq {{- \frac{1}{p\Delta}}{\log\left( {1 - P^{\max}} \right)}}}{\mu_{t} + \eta}} \geq {N_{t}\ {\forall t}}$${{or}:{N_{t} \leq N_{t}^{\max}}} = {{- \frac{1}{Mp\Delta}}{\log\left( {1 - P^{\max}} \right)}}$

according to some embodiments.

Process 600 includes performing an optimization to determine controldecisions for HVAC equipment of the HVAC system, and ultraviolet lightsof the HVAC system such that the one or more constraints are met and thecost is minimized (step 616), according to some embodiments. Step 616can be performed by optimization manager 412 by minimizing the objectivefunction subject to the one or more constraints (e.g., the temperature,humidity, etc., bounds and the infection probability constraint). Step616 can also include constructing the optimization problem andconstructing the optimization problem based on the objective function,the dynamic models (or the aggregated dynamic models), and the one ormore constraints. The control decisions can include a fresh-air fractionx for an AHU of the HVAC system (e.g., AHU 304), whether to turn on oroff the UV lights, etc.

Off-Line Optimization Process

Referring particularly to FIG. 7, a process for performing an off-lineoptimization to determine equipment configurations that minimize energyconsumption or cost and satisfy an infection probability constraint isshown, according to some embodiments. Process 700 may share similaritieswith process 600 but can be performed in an off-line mode (e.g., withoutdetermining control decisions or based on real-time sensor data) todetermine or assess various design decisions and provide designinformation to a building manager. Process 700 can be performed bycontroller 310 when configured for the off-line mode (as shown in FIG.5).

Process 700 includes steps 702-708 that can be the same as steps 602-608of process 600. However, while step 608 may be optional in process 600so that the optimization can be performed using a combination ofindividual dynamic models and aggregate dynamic models, step 708 may benon-optional in process 700. In some embodiments, using the aggregatedynamic models reduces a computational complexity of the optimizationfor process 700. Process 700 can be performed for a wide variety ofdesign parameters (e.g., different equipment configurations) whereasprocess 600 can be performed for a single equipment configuration (e.g.,the equipment configuration that process 600 is used to optimize).Therefore, it can be advantageous to use aggregate models in process 700to reduce a complexity of the optimization problem.

Process 700 includes populating the aggregated models using simulationdata (step 710). In some embodiments, step 710 is performed by modelmanager 416 using outputs from simulation database 424 (e.g., usingvalues of various parameters of the aggregate models that are stored insimulation database 424). In some embodiments, step 710 is performedusing known, assumed, or predetermined values to populate the aggregatedmodels.

Process 700 includes determining an objective function including a costof operating an HVAC system that serves the zones (step 712), anddetermining one or more constraints for the objective function includingan infection probability constraint (step 714), according to someembodiments. In some embodiments, step 712 and step 714 are similar toor the same as steps 612 and 614 of process 600.

Process 700 includes performing a sequence of one-step optimizations forvarious equipment configurations to estimate an operating costassociated with that equipment configuration (step 716), according tosome embodiments. In some embodiments, step 716 is performed byoptimization manager 412. Optimization manager 412 can constructdifferent optimization problems for different equipment configurationsusing the aggregate temperature model, the aggregated humidity model,the aggregated infectious quanta model, the one or more constraints, andthe objective function. In some embodiments, optimization manager 412 isconfigured to solve the optimization problems for the differentequipment configurations over a single time step. The results of theoptimizations problems can be output to results manager 418 fordisplaying to a user.

Process 700 includes outputting design suggestions or optimizationsresults to a user (step 718), according to some embodiments. In someembodiments, step 718 includes outputting costs associated withdifferent equipment configurations (e.g., equipment configurations thatinclude UV lights for disinfection and/or filters for disinfection) to auser (e.g., via a display device) so that the user (e.g., a buildingmanager) can determine if they wish to purchase additional disinfectionequipment (e.g., UV lights and/or filters). For example, step 718 caninclude operating a display to provide graph 800 (or a similar graph) toa user.

Although process 700 is described primarily as an “off-line” process, itshould be understood that process 700 is not limited to off-lineimplementations only. In some embodiments, process 700 can be used whencontroller 310 operates in an on-line mode (as described with referenceto FIGS. 4 and 6). In some embodiments, the results generated byperforming process 700 and/or the results generated when operatingcontroller 310 in the off-line mode (e.g., recommended equipmentconfigurations, recommended operating parameters, etc.) can be used toperform on-line control of HVAC equipment or perform other automatedactions. For example, controller 310 can use the recommended equipmentconfigurations to automatically enable, disable, or alter the operationof HVAC equipment in accordance with the recommended equipmentconfigurations (e.g., enabling the set of HVAC equipment associated withthe lowest cost equipment configuration identified by thesimulations/optimizations). Similarly, controller 310 can use therecommended operating parameters to generate and provide control signalsto the HVAC equipment (e.g., operating the HVAC equipment in accordancewith the recommended operating parameters).

In general, the controller 310 can use the optimization/simulationresults generated when operating controller 310 in the off-line mode togenerate design data including one or more recommended design parameters(e.g., whether to include or use UV lights 306 for disinfection, whetherto include or use filter 308 for disinfection, whether to usefresh/outdoor air for disinfection, a recommended type or rating of UVlights 306 or filter 308, etc.) as well as operational data includingone or more recommended operational parameters (e.g., the fraction offresh/outdoor air that should exist in the supply air provided to thebuilding zone, operating decisions for UV lights 306, an amount ofairflow to send to each building zone, etc.). The design data mayinclude a recommended equipment configuration that specifies which HVACequipment to use in the HVAC system to optimize the energy consumption,energy cost, carbon footprint, or other variable of interest whileensuring that a desired level of disinfection is provided.

Controller 310 can perform or initiate one or more automated actionsusing the design data and/or the operational data. In some embodiments,the automated actions include automated control actions such asgenerating and providing control signals to UV lights 306, AHU 304, oneor more VAV units, or other types of airside HVAC equipment that operateto provide airflow to one or more building zones. In some embodiments,the automated action include initiating a process to purchase or installthe recommended set of HVAC equipment defined by the design data (e.g.,providing information about the recommended set of HVAC equipment to auser, automatically scheduling equipment upgrades, etc.). In someembodiments, the automated actions include providing the design dataand/or the operational data to a user interface device (e.g., displaydevice 422) and/or obtaining user input provided via the user interfacedevice. The user input may indicate a desired level of disinfectionand/or a request to automatically update the results of theoptimizations/simulations based on user-selected values that define thedesired infection probability or level of disinfection. Controller 310can be configured to provide any of a variety of user interfaces(examples of which are discussed below) to allow a user to interact withthe results of the optimizations/simulations and adjust the operation ordesign of the HVAC system based on the results.

User Interfaces

Referring now to FIGS. 5 and 9, in some embodiments, user input device420 is configured to provide a user interface 900 to a user. An exampleof a user interface 900 that can be generated and presented via userinput device 420 is shown in FIG. 9. User interface 900 may allow a userto provide one or more user inputs that define which equipment areavailable in the building or should be considered for design purposes(e.g., filtration, UV, etc.) as well as the desired infectionprobability (e.g., low, medium, high, percentages, etc.). The inputsprovided via user interface 900 can be used by controller 310 to set upthe optimization problem or problems to be solved by optimizationmanager 412. For example, constraint generator 410 can use the inputsreceived via user interface 900 to generate the various bounds,boundaries, constraints, infection probability constraint, etc., thatare used by optimization manager 412 to perform the optimization. Aftercompleting all of the simulation scenarios, the results can be presentedto the user via the “Results” portion of user interface 900 that allowsthe user to explore various tradeoffs.

As an example, the “Building Options” portion of user interface 900allows the user to specify desired building and climate parameters suchas the square footage of the building, the city in which the building islocated, etc. The user may also specify whether UV disinfection and/oradvanced filtration should be considered in the simulation scenarios(e.g., by selecting or deselecting the UV and filtration options). The“Disinfection Options” portion of user interface 900 allows the user tospecify the desired level of disinfection or infection probability. Forexample, the user can move the sliders within the Disinfection Optionsportion of user interface 900 to define the desired level ofdisinfection for each month (e.g., low, high, an intermediate level,etc.). Alternatively, user interface 900 may allow the user to definethe desired level of disinfection by inputting infection probabilitypercentages, via a drop-down menu, by selecting or deselectingcheckboxes, or any other user interface element.

After specifying the desired parameters and clicking the “Run” button,optimization manager 412 may perform one or more simulations (e.g., bysolving one or more optimization problems) using the specifiedparameters. Once the simulations have completed, results may bedisplayed in the “Results” portion of user interface 900. The resultsmay indicate the energy cost, energy consumption, carbon footprint, orany other metric which optimization manager 412 seeks to optimize foreach of the design scenarios selected by the user (e.g., UV+Filtration,UV Only, Filtration Only, Neither). The results may also indicate thedaily infection probability for each of the design scenarios (e.g., meaninfection probability, minimum infection probability, maximum infectionprobability). In some embodiments, an initial simulation or simulationsare run using default settings for the disinfection options. In someembodiments, the results include equipment recommendations (e.g., useUV+Filtration, use UV Only, use Filtration Only, use Neither). Theresults of each simulation can be sorted to present the most optimalresults first and the least optimal results last. For example, userinterface 900 is shown presenting the simulation result with the leastenergy consumption first and the most energy consumption last. In otherembodiments, the results can be sorted by other criteria such asinfection probability or any other factor.

The user can adjust desired disinfection options on a monthly basis(e.g., by adjusting the sliders within the Disinfection Options portionof user interface 900), at which point the results may be re-calculatedby averaging over the appropriate subset of simulation instances, whichcan be performed in real time because the simulations need not repeated.Advantageously, this allows the user to adjust the disinfection optionsand easily see the impact on energy cost, energy consumption, carbonfootprint, etc., as well as the impact on infection probability for eachof the design scenarios. Additional display options beyond what is shownin FIG. 9 may be present in various embodiments, for example toselectively disable UV and/or filtration in certain months or toconsider worst-case instances for each month rather than mean values. Inaddition, various other graphical displays could be added to providemore detailed results. User interface 900 may initially presentoptimization results and/or equipment recommendations based on defaultsettings, but then the user is free to refine those settings andimmediately see updates to cost estimates and suggested equipment.

Although a specific embodiment of user interface 900 is shown in FIG. 9,it should be understood that this example is merely one possible userinterface that can be used in combination with the systems and methodsdescribed herein. In general, controller 310 can operate user inputdevice 420 to provide a user interface that includes various sliders,input fields, etc., to receive a variety of user inputs from the uservia user input device 420. In some embodiments, user input device 420 isconfigured to receive a desired level of disinfection, a desired levelof infection probability, etc., from the user and provide the desiredlevel of disinfection, or desired level of infection probability toconstraint generator 410 as the user input(s). In some embodiments, theuser interface includes a knob or a slider that allows the user toadjust between a level of energy savings and a level of infectioncontrol. For example, the user may adjust the knob or slider on the userinput device 420 to adjust the infection probability constraint (e.g.,to adjust thresholds or boundaries associated with the infectionprobability constraint).

In some embodiments, an infection spread probability is treated byconstraint generator 410 as a constraint, or as a value that is used byconstraint generator 410 to determine the infection probabilityconstraint. If a user desires to provide a higher level of disinfection(e.g., a lower level of infection spread probability) and therefore anincreased energy consumption or energy consumption cost, the user mayadjust the knob or slider on the user interface of user input device 420to indicate a desired trade-off between energy consumption and infectionprobability. Likewise, if the user desired to provide a lower level ofdisinfection (e.g., a higher level of infection spread probability) andtherefore a lower energy consumption or energy consumption cost, theuser may adjust the knob or slider on the user interface of the userinput device 420 to indicate such a desired tradeoff between energyconsumption or energy consumption cost and disinfection control.

In some embodiments, user input device 420 is configured to provideanalytics, data, display data, building data, operational data,diagnostics data, energy consumption data, simulation results, estimatedenergy consumption, or estimated energy consumption cost to the user viathe user interface of user input device 420. For example, resultsmanager 418 may operate the user input device 420 and/or the displaydevice 422 to provide an estimated energy consumption or energyconsumption cost to the user (e.g., results of the optimization ofoptimization manager 412 when operating in either the on-line oroff-line mode/configuration). In some embodiments, user input device 420and display device 422 are a same device (e.g., a touchscreen displaydevice, etc.) that are configured to provide the user interface, whilein other embodiments, user input device 420 and display device 422 areseparate devices that are configured to each provide their ownrespective user interfaces.

For example, controller 310 can perform the off-line or planning ordesign tool functionality as described in greater detail above inreal-time (e.g., as the user adjusts the knob or slider) to determine anestimated energy consumption or energy consumption cost given aparticular position of the knob or slider (e.g., given a particulardesired level of infection or disinfection control as indicated by theposition of the knob or slider). In some embodiments, controller 310 isconfigured to operate the user input device 420 and/or the displaydevice 422 to provide or display the estimated energy consumption orestimated energy consumption cost as the user adjusts the knob orslider. In this way, the user can be informed regarding an estimation ofcosts or energy consumption associated with a specific level ofdisinfection control (e.g., with a particular infection probabilityconstraint). Advantageously, providing the estimation of costs or energyconsumption associated with the specific level of disinfection controlto the user in real-time or near real-time facilitates the userselecting a level of disinfection control that provides sufficient ordesired disinfection control in addition to desired energy consumptionor energy consumption costs.

Pareto Optimization

Referring now to FIG. 10, a graph 1000 illustrating a Pareto searchtechnique which can be used by controller 310 is shown, according to anexemplary embodiment. In some cases, users may want a more detailedtradeoff analysis than merely comparing a set of optimization resultsfor a set of selected infection probabilities. For such cases,controller 310 may use a more detailed Pareto search that iterativelydetermines points on a Pareto front 1002 for an energy cost vs.infection probability tradeoff curve. By running additional simulations,this tradeoff curve can be plotted as accurately as possible so thatusers can fully evaluate the entire continuum of infectionprobabilities, (e.g., to look for natural breakpoints where additionaldisinfection probability begins to get more expensive).

To determine the points on the Pareto front 1002, controller 310 maystart with a small number of infection probabilities already simulatedfor a given month and plot them against monthly energy cost. Then,additional candidate infection probabilities can be selected (e.g., asthe points furthest from already completed simulations). Aftersimulating instances with the new infection probabilities, these pointsare added to the plot, and the process repeats to the desired accuracy.Many criteria for selecting new points are possible, but one possiblestrategy is to choose the midpoint of successive points with the largestarea (i.e., of the rectangle whose opposite corners are given by the twoexisting points) between them. This strategy prioritizes regions wherethe curve is changing rapidly and leads to efficient convergence.

As an example, consider the case in graph 1000. The goal is to obtain anapproximation of the true Pareto front 1002, which is illustrated inFIG. 10 for ease of explanation, but may not be truly known. Theinstances of the optimization run for the small number of infectionprobabilities result in the points marked with squares in graph 1000 forIteration 0. This gives a very coarse approximation of the true front.Controller 310 may then select new points in each iteration, run thosesimulations, and add those points to graph 1000. For example, the pointsmarked with diamond shapes in graph 1000 show the points selected forIteration 1 the points marked with triangles in graph 1000 show thepoints selected for Iteration 2, the points marked with invertedtriangles in graph 1000 show the points selected for Iteration 3, andthe points marked with circles in graph 1000 show the points selectedfor Iteration 4. By the end of Iteration 4, the empirical Pareto frontis a good approximation of the true front 1002, and of course additionaliterations can be performed to further improve accuracy. The empiricalPareto front generated using this technique can be used by controller300 to solve a Pareto optimization problem to determine an optimaltradeoff between the costs and benefits of selecting different infectionprobability values in the infection probability constraint.

In some embodiments, determining the infection probability constraint(e.g., to provide an optimal level of disinfection control, or anoptimal level of infection probability spread) and the resulting energyconsumption or energy consumption costs required for HVAC system 200 tooperate to achieve the infection probability constraint is a Paretooptimization problem. For example, at a certain point, additionaldisinfection control may require undesirably high energy consumption orenergy consumption costs. In some embodiments, controller 310 may solvea Pareto optimization problem given various inputs for the system todetermine one or more inflection points along a curve between cost(e.g., energy consumption or energy consumption cost) and a benefit(e.g., disinfection control, infection probability, disinfection, etc.)or to determine an optimal tradeoff between the cost and the benefit.

In some embodiments, controller 310 is configured to operate displaydevice 422 and/or user input device 420 to provide an infectionprobability constraint associated with the optimal tradeoff between thecost and the benefit. In some embodiments, controller 310 can operateaccording to various modes that can be selected by the user via the userinterface of user input device 420. For example, the user may opt for afirst mode where controller 310 solves the Pareto optimization problemto determine the infection probability constraint associated with theoptimal tradeoff point between the cost (e.g., the energy consumption orenergy consumption cost) and the benefit (e.g., the disinfectioncontrol, a provided level of disinfection, an infection probability,etc.). In the first mode, the controller 310 can automatically determinethe infection probability constraint based on the results of the Paretooptimization problem. In some embodiments, controller 310 still operatesdisplay device 422 to provide estimated, actual, or current energyconsumption or energy consumption costs and infection probabilityconstraints.

In a second mode, controller 310 can provide the user the ability tomanually adjust the tradeoff between the cost and the benefit (e.g., byadjusting the slider or knob as described in greater detail above). Insome embodiments, the user may select the desired tradeoff betweeninfection control and energy consumption or energy consumption costsbased on the provided estimations of energy consumption or energyconsumption costs.

In a third mode, controller 310 can provide the user additional manualabilities to adjust the infection probability constraint directly. Inthis way, the user may specifically select various boundaries (e.g.,linear boundaries if the infection probability constraint is implementedas a linear constraint as described in greater detail above) for theinfection probability constraint. In some embodiments, the user mayselect between the various modes (e.g., the first mode, the second mode,and/or the third mode).

It should be understood that while the Pareto optimization as describedherein is described with reference to only two variables (e.g., energyconsumption or energy consumption cost and disinfection control), thePareto optimization may also account for various comfort parameters orvariables (e.g., temperature and/or humidity of zones 206, eitherindividually or aggregated). In some embodiments, controller 310 mayalso operate display device 422 to provide various comfort parametersthat result from a particular position of the knob or slider that isprovided on the user interface of user input device 420. In someembodiments, additional knobs, sliders, input fields, etc., are alsoprovided on the user interface of user input device 420 to receivevarious inputs or adjustments for desired comfort parameters (e.g.,temperature and/or humidity). In some embodiments, controller 310 (e.g.,results manager 418) is configured to use the dynamic models fortemperature or humidity as described above to determine estimations ofthe various comfort parameters as the user adjusts the knobs or sliders(e.g., the knobs or sliders associated with disinfection control and/orenergy consumption or energy cost consumption). Similarly, controller310 can solve the Pareto optimization problem as a multi-variableoptimization problem to determine an inflection point or a Paretoefficiency on a surface (e.g., a 3d graph or a multi-variableoptimization) which provides an optimal tradeoff between cost (e.g., theenergy consumption, the energy consumption cost, etc.), comfort (e.g.,temperature and/or humidity), and disinfection control (e.g., theinfection probability constraint).

Configuration of Exemplary Embodiments

Although the figures show a specific order of method steps, the order ofthe steps may differ from what is depicted. Also two or more steps canbe performed concurrently or with partial concurrence. Such variationwill depend on the software and hardware systems chosen and on designerchoice. All such variations are within the scope of the disclosure.Likewise, software implementations could be accomplished with standardprogramming techniques with rule based logic and other logic toaccomplish the various connection steps, calculation steps, processingsteps, comparison steps, and decision steps.

The construction and arrangement of the systems and methods as shown inthe various exemplary embodiments are illustrative only. Although only afew embodiments have been described in detail in this disclosure, manymodifications are possible (e.g., variations in sizes, dimensions,structures, shapes and proportions of the various elements, values ofparameters, mounting arrangements, use of materials, colors,orientations, etc.). For example, the position of elements can bereversed or otherwise varied and the nature or number of discreteelements or positions can be altered or varied. Accordingly, all suchmodifications are intended to be included within the scope of thepresent disclosure. The order or sequence of any process or method stepscan be varied or re-sequenced according to alternative embodiments.Other substitutions, modifications, changes, and omissions can be madein the design, operating conditions and arrangement of the exemplaryembodiments without departing from the scope of the present disclosure.

As used herein, the term “circuit” may include hardware structured toexecute the functions described herein. In some embodiments, eachrespective “circuit” may include machine-readable media for configuringthe hardware to execute the functions described herein. The circuit maybe embodied as one or more circuitry components including, but notlimited to, processing circuitry, network interfaces, peripheraldevices, input devices, output devices, sensors, etc. In someembodiments, a circuit may take the form of one or more analog circuits,electronic circuits (e.g., integrated circuits (IC), discrete circuits,system on a chip (SOCs) circuits, etc.), telecommunication circuits,hybrid circuits, and any other type of “circuit.” In this regard, the“circuit” may include any type of component for accomplishing orfacilitating achievement of the operations described herein. Forexample, a circuit as described herein may include one or moretransistors, logic gates (e.g., NAND, AND, NOR, OR, XOR, NOT, XNOR,etc.), resistors, multiplexers, registers, capacitors, inductors,diodes, wiring, and so on).

The “circuit” may also include one or more processors communicablycoupled to one or more memory or memory devices. In this regard, the oneor more processors may execute instructions stored in the memory or mayexecute instructions otherwise accessible to the one or more processors.In some embodiments, the one or more processors may be embodied invarious ways. The one or more processors may be constructed in a mannersufficient to perform at least the operations described herein. In someembodiments, the one or more processors may be shared by multiplecircuits (e.g., circuit A and circuit B may comprise or otherwise sharethe same processor which, in some example embodiments, may executeinstructions stored, or otherwise accessed, via different areas ofmemory). Alternatively or additionally, the one or more processors maybe structured to perform or otherwise execute certain operationsindependent of one or more co-processors. In other example embodiments,two or more processors may be coupled via a bus to enable independent,parallel, pipelined, or multi-threaded instruction execution. Eachprocessor may be implemented as one or more general-purpose processors,application specific integrated circuits (ASICs), field programmablegate arrays (FPGAs), digital signal processors (DSPs), or other suitableelectronic data processing components structured to execute instructionsprovided by memory. The one or more processors may take the form of asingle core processor, multi-core processor (e.g., a dual coreprocessor, triple core processor, quad core processor, etc.),microprocessor, etc. In some embodiments, the one or more processors maybe external to the apparatus, for example the one or more processors maybe a remote processor (e.g., a cloud based processor). Alternatively oradditionally, the one or more processors may be internal and/or local tothe apparatus. In this regard, a given circuit or components thereof maybe disposed locally (e.g., as part of a local server, a local computingsystem, etc.) or remotely (e.g., as part of a remote server such as acloud based server). To that end, a “circuit” as described herein mayinclude components that are distributed across one or more locations.

The present disclosure contemplates methods, systems and programproducts on any machine-readable media for accomplishing variousoperations. The embodiments of the present disclosure can be implementedusing existing computer processors, or by a special purpose computerprocessor for an appropriate system, incorporated for this or anotherpurpose, or by a hardwired system. Embodiments within the scope of thepresent disclosure include program products comprising machine-readablemedia for carrying or having machine-executable instructions or datastructures stored thereon. Such machine-readable media can be anyavailable media that can be accessed by a general purpose or specialpurpose computer or other machine with a processor. By way of example,such machine-readable media can comprise RAM, ROM, EPROM, EEPROM, CD-ROMor other optical disk storage, magnetic disk storage or other magneticstorage devices, or any other medium which can be used to carry or storedesired program code in the form of machine-executable instructions ordata structures and which can be accessed by a general purpose orspecial purpose computer or other machine with a processor. Combinationsof the above are also included within the scope of machine-readablemedia. Machine-executable instructions include, for example,instructions and data which cause a general purpose computer, specialpurpose computer, or special purpose processing machines to perform acertain function or group of functions.

What is claimed is:
 1. A heating, ventilation, or air conditioning(HVAC) system, the HVAC system comprising: one or more processors; andmemory storing instructions that, when executed by the one or moreprocessors, cause the one or more processors to perform operationscomprising: performing a plurality of simulations for a plurality ofdifferent equipment configurations using a temperature model, aninfectious quanta model, and an infection probability to provideresults; using the results of the plurality of simulations, to provideat least one of design data comprising one or more recommended designparameters or operational data comprising one or more recommendedoperational parameters for the HVAC system; and initiating an automatedaction using at least one of the design data or the operational data. 2.The HVAC system of claim 1, wherein the operations further comprise:determining a dynamic humidity model for the one or more building zones;and performing the plurality of simulations using the dynamic humiditymodel to generate the results.
 3. The HVAC system of claim 1, whereinthe one or more recommended design parameters indicate whether toinclude disinfection lighting for disinfection in the HVAC system,whether to include an air filter for disinfection in the HVAC system,and whether to use fresh air for disinfection in the HVAC system.
 4. TheHVAC system of claim 1, wherein the one or more recommended designparameters comprise a recommended rating of an air filter for use in theHVAC system.
 5. The HVAC system of claim 1, wherein the automated actioncomprises presenting at least one of the design data or the operationaldata to a user via a user interface.
 6. The HVAC system of claim 1,wherein the plurality of simulations comprise at least two of: a firstsimulation in which the HVAC system includes disinfection lighting butdoes not include an air filter for disinfection; a second simulation inwhich the HVAC system includes the air filter but does not include thedisinfection lighting for disinfection; a third simulation in which theHVAC system includes both the disinfection lighting and the air filterfor disinfection; and a fourth simulation in which the HVAC systemincludes neither of the disinfection lighting nor the air filter fordisinfection.
 7. The HVAC system of claim 1, wherein the operationsfurther comprise: generating an infectious quanta constraint based on auser input indicating a desired a level of disinfection; performing atleast one of the plurality of simulations subject to the infectiousquanta constraint to generate an estimated cost of operating the HVACsystem; and presenting the estimated cost of operating the HVAC systemvia a user interface.
 8. The HVAC system of claim 1, wherein theoperations further comprise using the results of the plurality ofsimulations to provide a user interface that indicates a tradeoffbetween the infection probability and at least one of energy cost orenergy consumption.
 9. The HVAC system of claim 1, wherein therecommended operational parameters comprise a recommended control schemefor the HVAC system.
 10. A heating, ventilation, or air conditioning(HVAC) design tool for a HVAC system for a building, the HVAC designtool comprising: one or more processors; and memory storing instructionsthat, when executed by the one or more processors, cause the one or moreprocessors to perform operations comprising: performing a plurality ofsimulations for a plurality of different equipment configurations usinga temperature model, an infectious quanta model, and an infectionprobability; and using the simulations to provide a display indicating arelationship between the infection probability and at least one ofenergy cost or energy consumption.
 11. The HVAC design tool of claim 10,wherein the wherein the relationship is a tradeoff.
 12. The HVAC designtool of claim 10, wherein the display is provided based upon paretoanalysis.
 13. The HVAC design tool of claim 10, further comprising:using results of the plurality of simulations to provide at least one ofdesign data comprising one or more recommended design parameters or toprovide operational data comprising one or more recommended operationalparameters for the HVAC system; and initiating an automated action usingat least one of the design data or the operational data.
 14. The HVACdesign tool of claim 13, wherein performing the simulations comprisesoptimizing an objective function indicating a cost of operating the HVACsystem using one or more potential equipment configurations to provide adesired level of disinfection.
 15. The HVAC design tool of claim 14,wherein the desired level of disinfection is a user-selected value. 16.The HVAC design tool of claim 10, wherein the operations furthercomprise: generating an infectious quanta constraint based on a userinput indicating a desired a level of disinfection; performing thesimulation subject to the infectious quanta constraint to generate anestimated cost of operating the HVAC system; and presenting theestimated cost of operating the HVAC system via a user interface. 17.The HVAC design tool of claim 16, wherein the user input indicates atradeoff between a desired level of disinfection and energy cost, theenergy cost comprising at least one of an estimated energy consumptionof the HVAC system or an estimated monetary cost of the energyconsumption of the HVAC system.
 18. A method for providing design andoperating recommendations for a heating, ventilation, or airconditioning (HVAC) system to achieve a desired level of infectioncontrol in a building, the method comprising: obtaining a dynamictemperature model and a dynamic infectious quanta model for one or morebuilding zones; determining an infection probability; using the dynamictemperature model, the dynamic infectious quanta model, and theinfection probability to provide at least one of design recommendationsor operating recommendations to achieve the desired level of infectioncontrol; and operating a display to provide at least one of the designrecommendations or the operating recommendations to a user.
 19. Themethod of claim 18, wherein the design recommendations or the operatingrecommendations comprise at least one of: a recommended equipmentconfiguration of the HVAC system; recommended equipment specificationsof the HVAC system; a recommended filter rating of a filter of the HVACsystem; a recommended model of equipment of the HVAC system; or arecommended control scheme for the HVAC system.
 20. The method of claim19, wherein the display is provided based upon pareto analysis.